Keywords
Computer Science and Digital Science
 A2.1.1. Semantics of programming languages
 A2.1.4. Functional programming
 A2.1.7. Distributed programming
 A2.1.11. Proof languages
 A2.2. Compilation
 A2.4. Formal method for verification, reliability, certification
 A2.4.1. Analysis
 A2.4.2. Modelchecking
 A2.4.3. Proofs
 A2.5. Software engineering
 A4.5. Formal methods for security
 A7.2. Logic in Computer Science
 A8.4. Computer Algebra
Other Research Topics and Application Domains
 B6.1. Software industry
 B6.1.1. Software engineering
 B6.3.2. Network protocols
 B6.6. Embedded systems
1 Team members, visitors, external collaborators
Research Scientists
 Stephan Merz [Team leader, INRIA, Senior Researcher, HDR]
 Ioannis Filippidis [INRIA, Starting Research Position, until Aug 2022]
 Engel Lefaucheux [INRIA, ISFP]
 Thomas Sturm [CNRS, Senior Researcher, HDR]
 Sophie Tourret [INRIA, Researcher]
 Uwe Waldmann [Max Planck Society, Senior Researcher]
 Christoph Weidenbach [Max Planck Society, Senior Researcher, HDR]
Faculty Members
 Étienne André [UL, Professor, until Aug 2022, HDR]
 Horatiu Cirstea [UL, Professor, HDR]
 Marie DuflotKremer [UL, Associate Professor]
 Sergueï Lenglet [UL, Associate Professor]
 PierreÉtienne Moreau [UL, Professor, HDR]
 Victor Roussanaly [UL, ATER, from Oct 2022]
 Sorin Stratulat [UL, Associate Professor, HDR]
PostDoctoral Fellows
 Martin Bromberger [Max Planck Society]
 Zheng Cheng [UL]
 Sibylle Möhle [Max Planck Society, from Aug 2022]
 Hamid Rahkooy [Max Planck Society, until Oct 2022]
 Guillaume Verdier [UL]
PhD Students
 Thomas Bagrel [UL, CIFRE, from Apr 2022]
 Rosalie Defourne [UL, ATER, from Sep 2022]
 Rosalie Defourne [INRIA, until Aug 2022]
 Martin Desharnais [Max Planck Society]
 Fajar Haifani [Max Planck Society]
 Hendrik Leidinger [Max Planck Society]
 Lorenz Leutgeb [Max Planck Society]
 Dylan Marinho [UL]
 HansJörg Schurr [UL, ATER, until Aug 2022]
 Simon Schwarz [Max Planck Society, from Oct 2022]
Technical Staff
 Benjamin Loillier [INRIA, Engineer]
Interns and Apprentices
 Shapagat Bolat [Inria, Intern, from Mar 2022]
 Florent Krasnopol [Inria, Intern, from Jun 2022 until Jul 2022]
 Nurgul Osmonova [Inria, Intern, from Mar 2022 until Jun 2022]
 Vincent Trélat [UL, Intern, until Jul 2022]
 Zunaira Zaman [Inria, Intern, from Mar 2022 until Jun 2022]
Administrative Assistants
 Juline Brevillet [UL, from May 2022]
 Antoinette Courrier [UL, until Apr 2022]
 Sophie Drouot [INRIA]
Visiting Scientist
 Marian Ileana [University of Pitesti, from Nov 2022]
External Collaborators
 Jasmin Blanchette [Free University of Amsterdam, until Mar 2022]
 Pascal Fontaine [University of Liège, HDR]
2 Overall objectives
The VeriDis project team includes members of the MOSEL group at LORIA, the computer science laboratory in Nancy, and members of the research group Automation of Logic at MaxPlanckInstitut für Informatik in Saarbrücken. It is headed by Stephan Merz and Christoph Weidenbach. VeriDis was created in 2010 as a local research group of Inria Nancy – Grand Est and has been an Inria project team since July 2012.
The objectives of VeriDis are to contribute to advances in verification techniques, including automated and interactive theorem proving, and to make them available for the development and analysis of concurrent and distributed algorithms and systems, based on mathematically precise and practically applicable development methods. The techniques that we develop are intended to assist designers of algorithms and systems in carrying out formally verified developments, where proofs of relevant properties, as well as bugs, can be found with a high degree of automation.
Within this context, we work on techniques for automated theorem proving for expressive languages based on firstorder logic, with support for theories (fragments of arithmetic, set theory etc.) that are relevant for specifying algorithms and systems. Ideally, systems and their properties would be specified using highlevel, expressive languages, errors in specifications would be discovered automatically, and finally, full verification could also be performed completely automatically. Due to the fundamental undecidability of the problem, this cannot be achieved in general. Nevertheless, we have observed important advances in automated deduction in recent years, to which we have contributed. These advances suggest that a substantially higher degree of automation can be achieved over what is available in today's tools supporting deductive verification. Our techniques are developed within SMT (satisfiability modulo theories) solving and firstorder logic reasoning, the two main frameworks of contemporary automated reasoning that have complementary strengths and weaknesses, and we are interested in making them converge when appropriate. Techniques developed within the symbolic computation domain, such as algorithms for quantifier elimination for appropriate theories, are also relevant, and we are working on integrating them into our portfolio of techniques. In order to handle expressive input languages, we are working on techniques that encompass tractable fragments of higherorder logic, for example for specifying inductive or coinductive data types, for automating proofs by induction, or for handling collections defined through a characteristic predicate.
Since full automatic verification remains elusive, another line of our research targets interactive proof platforms. We intend these platforms to benefit from our work on automated deduction by incorporating powerful automated backends and thus raise the degree of automation beyond what current proof assistants can offer. Since most conjectures stated by users are initially wrong (due to type errors, omitted hypotheses or overlooked border cases), it is also important that proof assistants be able to detect and explain such errors rather than letting users waste considerable time in futile proof attempts. Moreover, increased automation must not come at the expense of trustworthiness: skeptical proof assistants expect to be given an explanation of the proof found by the backend prover that they can certify.
Model checking is also an established and highly successful technique for verifying systems and for finding errors. Our contributions in this area more specifically target quantitative, in particular timed or probabilistic systems. A specificity of VeriDis is notably to consider partially specified systems, using parameters, in which case the verification problem becomes the synthesis of suitable parameter valuations.
Our methodological and foundational research is accompanied by the development of efficient software tools, several of which go beyond pure research prototypes: they have been used by others, have been integrated in verification platforms developed by other groups, and participate in international competitions. We also validate our work on verification techniques by applying them to the formal development of algorithms and systems. We mainly target highlevel descriptions of concurrent and distributed algorithms and systems. This class of algorithms is by now ubiquitous, ranging from multi and manycore algorithms to large networks and cloud computing, and their formal verification is notoriously difficult. Targeting high levels of abstraction allows the designs of such systems to be verified before an actual implementation has been developed, contributing to reducing the costs of formal verification. The potential of distributed systems for increased resilience to component failures makes them attractive in many contexts, but also makes formal verification even more important and challenging. Our work in this area aims at identifying classes of algorithms and systems for which we can provide guidelines and identify patterns of formal development that makes verification less an art and more an engineering discipline. We mainly target components of operating systems, distributed and cloud services, and networks of computers or mobile devices.
Beyond formal system verification, we pursue applications of some of the symbolic techniques that we develop in other domains. We have observed encouraging success in using techniques of symbolic computation for the qualitative analysis of biological and chemical networks described by systems of ordinary differential equations that were previously only accessible to largescale simulation. Such networks include biological reaction networks as they occur with models for diseases such as diabetes or cancer. They furthermore include epidemic models such as variants and generalizations of SEIR1 models, which are typically used for Influenza A or Covid19. This work is being pursued within a largescale interdisciplinary collaboration. It aims for our work grounded in verification to have an impact on the sciences, beyond engineering, which will feed back into our core formal methods community.
3 Research program
3.1 Automated and Interactive Theorem Proving
The VeriDis team gathers experts in techniques and tools for automatic deduction and interactive theorem proving, and specialists in methods and formalisms designed for the development of trustworthy concurrent and distributed systems and algorithms. Our common objective is twofold: first, we wish to advance the state of the art in automated and interactive theorem proving, and their combinations. Second, we work on making the resulting technology available for the computeraided verification of distributed systems and protocols. In particular, our techniques and tools are intended to support sound methods for the development of trustworthy distributed systems that scale to algorithms relevant for practical applications.
VeriDis members from Saarbrücken are developing the Spass 10workbench. It currently consists of one of the leading automated theorem provers for firstorder logic based on the superposition calculus 66, a theory solver for linear arithmetic 2, a CDCL2 based satisfiability solver and a propositional converter to clausal normal form. Recently we have extended it to a Datalog hammer solving universal and existential queries with respect to a Horn BernaysSchoenfinkel theory modulo linear arithmetic 72, 71.
In a complementary approach to automated deduction, VeriDis members from Nancy work on techniques for integrating reasoners for specific theories. They develop veriT1, an SMT 3 solver that combines decision procedures for different fragments of firstorder logic. The veriT solver is designed to produce detailed proofs; this makes it particularly suitable as a component of a robust cooperation of deduction tools.
Finally, VeriDis members design effective quantifier elimination methods and decision procedures for algebraic theories, supported by their efficient implementation in the Redlog system 5.
An important objective of this line of work is the integration of theories in automated deduction. Typical theories of interest, including fragments of arithmetic, are difficult or impossible to express in firstorder logic. We therefore explore efficient, modular techniques for integrating semantic and syntactic reasoning methods, develop novel combination results and techniques for quantifier instantiation. These problems are addressed from both sides, i.e. by embedding decision procedures into the superposition framework or by allowing an SMT solver to accept axiomatizations for plugin theories. We also develop specific decision procedures for theories such as nonlinear real arithmetic that are important when reasoning about certain classes of (e.g., realtime) systems but that also have interesting applications beyond verification.
We rely on interactive theorem provers for reasoning about specifications at a high level of abstraction when fully automatic verification is not (yet) feasible. An interactive proof platform should help verification engineers lay out the proof structure at a sufficiently high level of abstraction; powerful automatic plugins should then discharge the resulting proof steps. Members of VeriDis have ample experience in the specification and subsequent machineassisted, interactive verification of algorithms. In particular, we participate in a project at the joint Microsoft ResearchInria Centre on the development of methods and tools for the formal proof of specifications written in the TLA+81 language. Our prover relies on a declarative proof language, and calls upon several automatic backends 4. Trust in the correctness of the overall proof can be ensured when the backends provide justifications that can be checked by the trusted kernel of a proof assistant. During the development of a proof, most obligations that are passed to the prover actually fail – for example, because necessary information is not present in the context or because the invariant is too weak, and we are interested in explaining failed proof attempts to the user, in particular through the construction of countermodels.
Members of VeriDis formalize a framework in the proof assistant Isabelle/HOL for representing the correctness and completeness of automated theorem provers. This work encompasses proof calculi such as ordered resolution or superposition, as well as concrete prover architectures such as Otter or DISCOUNT loops. It also covers the most recent splitting techniques that bring proof calculi closer to SMT solvers.
3.2 Formal Methods for Developing and Analyzing Algorithms and Systems
Theorem provers are not used in isolation, but they support the application of sound methodologies for modeling and verifying systems. In this respect, members of VeriDis have gained expertise and recognition in making contributions to formal methods for concurrent and distributed algorithms and systems 3, 8, and in applying them to concrete use cases. In particular, the concept of refinement63, 67, 84 in statebased modeling formalisms is central to our approach because it allows us to present a rational (re)construction of system development. An important goal in designing such methods is to establish precise proof obligations, many of which can be discharged by automatic tools. This requires taking into account specific characteristics of certain classes of systems and tailoring the model to concrete computational models. Our research in this area is supported by carrying out case studies for academic and industrial developments. This activity benefits from and influences the development of our proof tools.
In this line of work, we investigate specific development and verification patterns for particular classes of algorithms, in order to reduce the work associated with their verification. We are also interested in applications of formal methods and their associated tools to the development of systems that underlie specific certification requirements in the sense of, e.g., Common Criteria. Finally, we are interested in the adaptation of model checking techniques for verifying actual distributed programs, rather than highlevel models.
Today, the formal verification of a new algorithm is typically the subject of a PhD thesis, if it is addressed at all. This situation is not sustainable given the move towards more and more parallelism in mainstream systems: algorithm developers and system designers must be able to productively use verification tools for validating their algorithms and implementations. On a high level, the goal of VeriDis is to make formal verification standard practice for the development of distributed algorithms and systems, just as symbolic model checking has become commonplace in the development of embedded systems and as security analysis for cryptographic protocols is becoming standard practice today. Although the fundamental problems in distributed programming are wellknown, they pose new challenges in the context of modern system paradigms, including adhoc and overlay networks or peertopeer systems, and they must be integrated for concrete applications.
Model checking
The paradigm of model checking is based on automatically verifying properties over a formal model of a system, using mathematical foundations. Model checking, while useful and highly successful in practice, can encounter the infamous state space explosion problem. One direction of VeriDis therefore addresses the efficiency of model checking, by proposing new algorithms or heuristics to speed up analysis. We notably focus on the quantitative setting (time, probabilities), and more specifically on the parametric paradigm where some quantitative constants are unknown, and the goal becomes to synthesize suitable valuations. A recent application of the VeriDis team is that of opacity (in the more general field of cybersecurity), addressed using model checking. The team considers a novel definition of opacity in timed automata, where an attacker has only access to the execution time; several recent works address this direction.
3.3 Verification and Analysis of Dynamic Properties of Biological Systems
The unprecedented accumulation of information in biology and medicine during the last 20 years led to a situation where any new progress in these fields is dependent on the capacity to model and make sense of large data. Until recently, foundational research was concerned with simple models of 2 to 5 ordinary differential equations. The analysis of even such simple models was sufficiently involved that it resulted in one or several scientific publications for a single model. Much larger models are built today to represent cell processes, explain and predict the origin and evolution of complex diseases or the differences between patients in precision and personalized medicine. For instance, the biomodels.net model repository 82 contains thousands of handbuilt models of up to several hundreds of variables. Numerical analysis of large models requires an exhaustive scan of the parameter space or the identification of the numerical parameters from data. Both are infeasible for large biological systems because parameters are largely unknown and because of the curse of dimensionality: data, even rich, become rapidly sparse when the dimensionality of the problem increases. On these grounds, VeriDis researchers aim at formal symbolic analysis instead of numerical simulation.
As an illustration of the approach, consider BIOMD0000000716 in the abovementioned BioModels database, which models the transmission dynamics of subtype H5N6 of the avian Influenza A virus in the Philippines in August 2017 83. This model describes four species (susceptible/infected bird or human) together with their dynamics. Using purely symbolic algorithms, we obtain a decomposition of the dynamics into three subsystems ${T}_{1}$, ${T}_{2}$, and ${T}_{3}$ with attractive manifolds ${\mathcal{M}}_{1}$, ${\mathcal{M}}_{2}$ and ${\mathcal{M}}_{3}$, and the constant factors appearing in the corresponding differential equations indicate that the system ${T}_{2}$ is 125 times slower than ${T}_{1}$, and that ${T}_{3}$ is another 125 times slower.
This multiple time scale reduction emphasizes a cascade of successive relaxations of model variables. Figure 1(a) shows the surface of ${\mathcal{M}}_{1}$ projected into 3D space, with the line and the dot representing the submanifolds ${\mathcal{M}}_{2}$ and ${\mathcal{M}}_{3}$. Figure 1(b) illustrates the direction field of ${T}_{1}$ projected into 2D space. The curve corresponds to ${\mathcal{M}}_{1}$, indicating that the population of susceptible birds relaxes and that these variables reach quasisteady state values. Figure 1(c) represents the direction field of ${T}_{2}$ on ${\mathcal{M}}_{1}$ projected into 2D space. The line corresponds to ${\mathcal{M}}_{2}$, showing the relaxation of the population of infected birds. Finally, figure 1(d) shows the direction field of ${T}_{3}$ on ${\mathcal{M}}_{2}$ projected into 2D space. The dot corresponds to ${\mathcal{M}}_{3}$, indicating the relaxation of the populations of susceptible and infected humans to a stable steady state.
The computation time is less than a second. The computation is based on massive SMT solving over various theories, including QF_LRA for tropicalizations, QF_NRA for testing Hurwitz conditions on eigenvalues, and QF_LIA for finding sufficient differentiability conditions for hyperbolic attractivity of critical manifolds. Gröbner reduction techniques are used for final algebraic simplification 80. Observe that numerical simulation would not be able to provide such a global analysis of the overall system, even in the absence of symbolic parameters, as is the case in our rather simple example.
4 Application domains
Distributed algorithms and protocols are found at all levels of computing infrastructure, from manycore processors and systems on chip to widearea networks. We are particularly interested in the verification of algorithms that are developed for supporting novel computing paradigms, including adhoc networks that underly mobile and lowpower computing or overlay networks, peertopeer networks that provide services for telecommunication, or cloud computing services. Computing infrastructure must be highly available and is ideally invisible to the end user, therefore correctness is crucial. One should note that standard problems of distributed computing such as consensus, group membership or leader election have to be reformulated for the dynamic context of these modern systems. We are not ourselves experts in the design of distributed algorithms, but we work together with domain experts on designing formal models of these protocols, and on verifying their properties. These cooperations help us focus on concrete algorithms and ensure that our work is relevant to the distributed algorithm community.
Our work on symbolic procedures for solving polynomial constraints finds applications beyond verification. In particular, we have been working in interdisciplinary projects with researchers from mathematics, computer science, systems biology, and system medicine on the analysis of reaction networks and epidemic models in order to infer principal qualitative properties. Our techniques complement numerical analysis techniques and are validated against collections of models from computational biology.
The team uses extensions of timed automata (such as parametric timed automata 64) as an underlying formalism to solve practical questions. Our work on parametric timed automata is partly motivated by applications in cybersecurity, notably within the ANRNRF ProMiS project (cf. section 9.1). Foundational decidability results 11, 28 and novel notions of noninterference and opacity for this class of automata allow us, for example, to determine the maximal frequency of attacker actions for the attack to succeed (i.e., so that these actions remain invisible to the external observer). Several software artefacts were implemented by the team in this domain 65.
5 Highlights of the year
5.1 Awards
Alexander Bentkamp, a former PhD student at VU Amsterdam cosupervised by Jasmin Blanchette and Uwe Waldmann, received the Ackermann award of the European Association for Computer Science Logic, the Beth Award of the Association for Logic, Language and Information, the McCune award at CADE, and the dissertation award of the Institute for Programming Research and Algorithmics (IPA) for his PhD thesis 69.
Fajar Haifani received the DL 2022 Best Student Paper Award for the paper “Connectionminimal Abduction in EL via translation to FOL” 42.
Sophie Tourret has been recognized as a distinguished PC member of IJCAIECAI 2022, for the quality of her reviews (ranked in the top 3%).
6 New software and platforms
6.1 New software
6.1.1 IMITATOR

Name:
IMITATOR

Keywords:
Verification, Parametric model, Parameter synthesis, Model Checking, Model Checker, Timed automata

Functional Description:
IMITATOR is a software tool for parametric verification and robustness analysis of realtime systems with parameters. It relies on the formalism of networks of parametric timed automata, augmented with integer variables and stopwatches.

News of the Year:
Two new heuristics (merging and zone extrapolation) were implemented, with very interesting results in terms of efficiency. A very large extension of the syntax was performed, allowing new types (basic types, but also lists, arrays, stacks…), user defined functions over these types, etc. New applications to cybersecurity were analyzed.
 URL:
 Publications:

Contact:
Etienne Andre

Participants:
Etienne Andre, Jaime Eduardo Arias Almeida

Partner:
Loria
6.1.2 Redlog

Name:
Reduce Logic System

Keywords:
Computer algebra system (CAS), Firstorder logic, Constraint solving, Quantifier Elimination

Functional Description:
Redlog is an integral part of the interactive computer algebra system Reduce. It supplements Reduce's comprehensive collection of powerful methods from symbolic computation by supplying more than 100 functions on firstorder formulas.
Redlog generally works with interpreted firstorder logic in contrast to free firstorder logic. Each firstorder formula in Redlog must exclusively contain atoms from one particular Redlogsupported theory, which corresponds to a choice of admissible functions and relations with fixed semantics. Redlogsupported theories include Nonlinear Real Arithmetic (Real Closed Fields), Presburger Arithmetic, Parametric QSAT (quantified satisfiability solving), and many more.

News of the Year:
Parts of the Redlog code are more than 25 years old now. Version 1 of the underlying computer algebra system Reduce has been published even more than 50 years ago. In 2018 we therefore started to go for major revisions and improvements of Redlog's software architecture, which are still under way.
Our principal design goal is more simplicity for the sake of better longterm maintainability. Technically we now favor keeping state spaces in explicit mutable data structures rather than on the recursion stack. Although not directly supported by the underlying Lisp system, we use object oriented ideas and approaches to the extent possible.
 URL:

Contact:
Thomas Sturm

Participants:
Thomas Sturm, Andreas Dolzmann, Melanie Achatz, Marek Kosta, Aless Lasaruk, Herbert Melenk, Winfried Neun, Andreas Seidl, Christoph Zengler, Volker Weispfenning
6.1.3 REDUCE F5

Name:
A REDUCE Package for Computing Gröbner Bases Using F5

Keywords:
Symbolic computation, Gröbner bases

Functional Description:
F5 is a package for the computation of Gröbner Bases using Faugère's F5 algorithm. It uses multivariate rational functions as the coefficient field. The package is compatible with existing REDUCE term orderings, as used with the GROEBNER package and the CGB package.
From an Automated Reasoning viewpoint this offers a decision procedure for algebraically closed fields (including the complex numbers). The code has been designed with possible future generalization to the formal treatment of the coefficients as parameters and comprehensive Gröbner Bases in mind, which, in combination with other components of REDUCE, namely Redlog, would yield quantifier elimination and decision procedures for algebraically closed fields (including the complex numbers) as well as for real closed fields (including the real numbers).

News of the Year:
REDUCE F5 has been launched as a part of the regular REDUCE distribution on SourceForge.
 URL:

Contact:
Thomas Sturm

Participants:
Alexander Demin, Thomas Sturm, Hamid Rahkooy
6.1.4 SPASS Workbench

Name:
SPASS Automated Reasoning Workbench

Keywords:
Decision, Linear Systems Solver

Functional Description:
The SPASS Workbench is a collection of tools for various reasoning tasks in logic. It currently comprises the firstorder theorem prover SPASS, a decision procedure for linear (mixed) arithmetic SPASSIQ, a satisfiability modulo theory (SMT) solver for linear (mixed) arithmetic, a propositional satisfiability (SAT) solver SPASSSAT and a propositional conjunctive normal form converter SPASSCNF. In preparation is a solver SPASSSPL for a fragment we call SUPERLOG, which is the firstorder Bernays Schoenfinkel class extended with linear arithmetic.

News of the Year:
We now published the SAT solver SPASSSAT and the propositional CNF converter SPASSCNF.
 URL:
 Publications:

Contact:
Christoph Weidenbach

Participants:
Martin Bromberger, Christoph Weidenbach
6.1.5 ECyclist

Keyword:
Cyclic proofs

Functional Description:
Checking the soundness of cyclic induction reasoning for firstorder logic with inductive definitions (FOLID) is decidable but the standard checking method is based on an exponential complement operation for Büchi automata. We devised a polynomial method “semideciding” this problem in a paper presented at the CiSS2019 conference (Circularity in Syntax and Semantics). ECyclist is an extension of the Cyclist prover (http://www.cyclistprover.org/) that integrates this method. It successfully checked all the proofs included in the Cyclist distribution. The implementation details have been presented at SCSS 2021 (ID HAL: hal02464242).
 URL:

Contact:
Sorin Stratulat
6.1.6 TLAPS

Name:
TLA+ proof system

Keyword:
Proof assistant

Functional Description:
TLAPS is a platform for developing and mechanically verifying proofs about specifications written in the TLA+ language. The TLA+ proof language is hierarchical and explicit, allowing a user to decompose the overall proof into proof steps that can be checked independently. TLAPS consists of a proof manager that interprets the proof language and generates a collection of proof obligations that are sent to backend verifiers. The current backends include the tableaubased prover Zenon for firstorder logic, Isabelle/TLA+, an encoding of TLA+ set theory as an object logic in the logical framework Isabelle, an SMT backend designed for use with any SMTlib compatible solver, and an interface to a decision procedure for propositional temporal logic.
 URL:

Contact:
Stephan Merz

Participants:
Damien Doligez, Stephan Merz, Ioannis Filippidis

Partner:
Microsoft
6.1.7 veriT

Keywords:
Automated deduction, Formula solving, Verification

Functional Description:
VeriT is an open, trustable and efficient SMT (Satisfiability Modulo Theories) solver. It comprises a propositional satisfiability (SAT) solver, an efficient decision procedure for uninterpreted symbols based on congruence closure, a simplexbased decision procedure for linear arithmetic, and instantiationbased quantifier reasoning.

News of the Year:
Efforts in 2022 have been focused on higherorder logic, and better proof production. Achievements in 2022 are essentially around proof production, which makes veriT particularly suitable for integration within skeptical proof assistants. Code refactoring is envisioned for the future, to better accommodate the role of the solver as a platform for testing new ideas. Even if the veriT solver participated in the SMT competition http://www.smtcomp.org like previous years, the improvement on this incarnation of the solver have been minimal, and the performances have not improved compared to 2021.
We target applications where validation of formulas is crucial, such as proof about specifications written in the B or TLA+ languages, and we work together with the developers of the respective verification platforms to make veriT even more useful in practice. The solver is available as a plugin for the Rodin platform, and it is integrated within Atelier B.
veriT is also a prototype platform for ideas developed within the Matryoshka project, aiming at greater availability of automated reasoning for proof assistants.
 URL:

Contact:
Pascal Fontaine

Participants:
Pascal Fontaine, HansJörg Schurr, Sophie Tourret

Partner:
Université de Lorraine
6.2 New platforms
6.2.1 ODEbase
Participants: Thomas Sturm.

Name:
Online Database of Biomodels Involving Ordinary Differential Equations

Keywords:
Automated reasoning, Dynamical systems, Interdisciplinary research, Qualitative analysis

Scientific Description:
Symbolic Computation and Automated Reasoning allow qualitative answers to biological questions. Qualitative methods analyze dynamical input systems as formal objects, in contrast to investigating only a subset of the state space, as is the case with numerical simulation. A common format used in mathematical modeling of biological processes is the Systems Biology Markup Language SBML. However, symbolic tools and libraries have a different set of requirements for their input data than their numerical counterparts. The use of SBML data in Symbolic Computation and Automated Reasoning requires significant preprocessing that combines automated translation steps with human interaction and expertise. ODEbase provides preprocessed input data derived from established existing biomodels.

Functional Description:
SBML, which is technically an XML instance, has been designed as a very liberal format, and contributors of models are primarily researchers with their key expertise in the natural sciences. This creates a situation where SBML features are used in unexpected ways in general. A sound presentation of corresponding models outside the SMBL framework then requires expertise in the life sciences as well as mathematical competence, primarily in algebra and in dynamical systems. Technically we use a set of Python tools, which we have developed for the semiautomatic conversion of SBML models. Since the conversion process is not fully automatic and our resources are limited, we focus on models that we identify as interesting for Symbolic Computation and Automated Reasoning approaches. Our principal source of models is the renowned online database biomodels.net.
 News of the Year:
 URL:
 Publications:

Contact:
Thomas Sturm

Partners:
Christoph Lüders, University of Bonn, Germany, Ovidiu Radulescu, University of Montpellier, France.
7 New results
7.1 Automated and Interactive Theorem Proving
Participants: Jasmin Christian Blanchette, Martin Bromberger, Rosalie Defourné, Martin Desharnais, Ioannis Filippidis, Pascal Fontaine, Fajar Haifani, Hendrik Leidinger, Lorenz Leutgeb, Stephan Merz, Sibylle Möhle, HansJörg Schurr, Simon Schwarz, Sorin Stratulat, Sophie Tourret, Marco Voigt, Uwe Waldmann, Christoph Weidenbach.
7.1.1 Contributions to SMT Techniques
Quantifier Handling in HigherOrder SMT.
Joint work with Haniel Barbosa (Univ. Federal de Miras Gerais, Brazil).
SMT solvers have throughout the years been able to cope with increasingly expressive logics, from ground formulas to full firstorder logic (FOL). In the past, we proposed a pragmatic extension for SMT solvers to support higherorder logic reasoning natively without compromising performance on FOL reasoning, thus leveraging the extensive research and implementation efforts dedicated to efficient SMT solving. However, the higherorder SMT solvers resulting from this work are not as effective as we would expect given their performances in firstorder logic. We believe this comes from the fact that only the core of the SMT solver has been extended, ignoring in particular the modules for quantifier instantiation.
This motivated us to start working on an extension of the main quantifierinstantiation approach (congruence closure with free variables, CCFV) to higherorder logic in 2020. This work is still ongoing. We are working on an encoding of the CCFV higherorder problem into a set of SAT constraints. In 2020, we concentrated our efforts mainly on the theory, to prove the soundness and completeness of our approach. In 2021, as a first step towards an implementation, we designed precise pseudocode for all elements of CCFV computation. In 2022, these algorithms were implemented in a C++ library, and they were tested on benchmarks from the SMTlib collection. Future works involve thorough testing of the library, improvements, and release under an opensource permissive license.
Proofs for SMT.
We previously developed a framework for processing formulas in automatic theorem provers, with generation of detailed proofs that can be checked by external tools, including skeptical proof assistants. The main components are a generic contextual recursion algorithm and an extensible set of inference rules. Clausification, Skolemization, theoryspecific simplifications, and expansion of `let' expressions are instances of this framework. With suitable data structures, proof generation adds only a lineartime overhead, and proofs can be checked in linear time. We implemented the approach in the SMT solver veriT. This allowed us to dramatically simplify the code base while increasing the number of problems for which detailed proofs can be produced. Our publication at CADE 2021 88 demonstrates the excellent results of our approach, building on our previous work on proof formats for SMT and on proof reconstruction within the proof assistant Isabelle/HOL (e.g., 76). Our proof format was moreover the basis for the standard Alethe format 87, which is now getting adopted by the community. In 2022, the format was further polished, also to accommodate the needs of other SMT solvers adopting the format.
This is one of the main contributions, besides techniques for quantifier instantiation and strategy learning, of HansJörg Schurr's PhD thesis 52, defended in October 2022. During his postdoctoral research in the cvc5 team (Iowa and Stanford), HansJörg Schurr will continue to work notably on proofs for SMT.
7.1.2 Automated reasoning techniques beyond SMT
Extensions of a formal framework for automated reasoning.
We are part of a group developing a framework for formal refutational completeness proofs of abstract provers that implement automated reasoning calculi, especially calculi based on saturation such as ordered resolution and superposition. In previous work, we published a framework that fully captures the dynamic aspects of proof search with a saturation calculus. This framework covers clause splitting as supported by modern superposition provers with the help of a SAT solver. In particular, our formalization revealed some completeness issues with the theorem prover Vampire.
This year, we extended the Isabelle formalization by representations of the main loops of saturationbased theorem provers and their fairness conditions. In the process, we found and repaired several issue with the (in fact, our own) description of the Zipperposition loop, a novel loop that handles inferences producing an infinite stream of conclusions. In parallel, Martin Desharnais, for his PhD thesis, is working on an instantiation of this framework for the superposition calculus as formalized by Nicolas Peltier in the Archive of Formal Proof, a repository of Isabelle/HOL mechanizations 85. We also made progress on the Isabelle/HOL mechanization of the framework with clause splitting. Florent Krasnopol, a student of ENS Saclay, contributed to this endeavor for his firstyear internship. The two last pieces of work are still ongoing, while the first one has been completed in 2022 and a conference submission is being prepared on it.
Efficient implementation of superposition for higherorder logic.
In previous work, we designed a superposition calculus for higherorder logic and implemented it in a prototype called Zipperposition. Now, we designed and developed an extension of the highperformance firstorder prover E 86 with this higherorder calculus. When extending E, we used the extensive experience with Zipperposition to choose a set of effective rules that could easily be retrofitted into an originally firstorder prover. Challenges included accommodating $\lambda $terms in E's term representation, extending E by a higherorder unification procedure that can return multiple unifiers instead of a single one, and adapting the superposition rule to higherorder logic. A guiding principle for the design of our extension was gracefulness: we made sure that our changes do not impact the strong firstorder performance of E.
E helped us win the firstplace trophy at the CADE ATP System Competition (CASC), ahead of Zipperposition, in the Sledgehammer division of the 2022 edition of the competition. This confirms that an optimized implementation inside a competitive prover such as E, SPASS, or Vampire can outperform existing higherorder automated provers. A publication on this research has just been accepted and will be presented at the TACAS 2023 conference.
Relevance of clauses for resolution.
A clause is relevant for a refutation with respect to an unsatisfiable clause set if it occurs in all refutation proofs. It is semirelevant if it occurs in at least one refutation proof. We have shown that the question whether a clause $C$ is semirelevant can be reduced to the question whether there exists a setofsupport (SOS) refutation whose set of support is the singleton $\left\{C\right\}$77. To this end we generalized and finalized the wellknown completeness result on SOS resolution 61: SOS resolution is complete if and only if there exists a resolution refutation with one of the clauses out of the SOS. The notion of semirelevance is in particular useful to explain the contribution of a clause or formula to a specific consequence. For independent clause sets this syntactic notion of semirelevance has a semantic counterpart. A clause is semantically semirelevant if it contributes to the overall set of conflict literals 43. A conflict literal for some clause set is a literal where the literal and its negation are both consequences of satisfiable subsets of the clause set.
SCL for firstorder logic with and without equality.
We previously showed that the SCL (Clause Learning from Simple Models) calculus can be successfully applied through a Datalog hammer to firstorder logic modulo theories 34. It was on open question whether SCL can be effectively extended to firstorder logic with equality. It requires an interpretation of the simple ground model assumption with respect to equality. We could show that all syntactic operations on the simple ground model assumption can be lifted modulo equality and eventually be incorporated in a sound, complete, and effective SCL calculus for full firstorder logic with equality 46. In parallel, a mechanization effort for SCL without equality in Isabelle/HOL has been started by Martin Desharnais, as part of his PhD.
Certification of FOL${}_{\text{ID}}$ cyclic proofs.
Cyclic induction is a powerful reasoning technique that consists in blocking the proof development of certain subgoals already encountered during the proof process. In the setting of firstorder logic with inductive definitions and equality (FOL${}_{\text{ID}}$), cyclic proofs can be built automatically by the Cyclist prover, but their implementations are errorprone and the human validation may be tedious.
We developed techniques for checking, using Coq, the cyclic proofs produced by ECyclist (cf. section 6.1), an extension of the Cyclist theorem prover, relying on the general Noetherian induction principle that is available in Coq. In this way, cyclic FOL${}_{\text{ID}}$ proofs can be certified mechanically and automatically. Moreover, Coq users can directly perform cyclic induction reasoning. We successfully certified the ECyclist proofs of the FOL${}_{\text{ID}}$ examples included in the official distribution of the release CSLLICS14 of Cyclist, as well as the 2Hydra problem. The datasets generated during and/or analyzed during the current study, in particular, the full Coq specifications and proof scripts, are archived and made available on the Web.
Abduction for Description Logics.
Abduction is the process of explaining new observations using background knowledge. It is central to knowledge discovery and knowledge processing and has been intensely studied in various domains such as artificial intelligence, philosophy and logic. In the description logic literature, abduction has received little attention, despite being recognised as important for ontology repair, query update and matchmaking.
As part of his PhD, Fajar Haifani finalized in 2022 a technique for abduction in the lightweight description logic $\mathrm{\mathcal{E}\mathcal{L}}$, that specializes in representing subset inclusions and membership. His approach consists in translating the problem to firstorder logic to harness the power of the automated deduction tool SPASS to produce prime implicates, i.e., most general consequences, from which the solutions of the abduction problem can be reconstructed. The complete method, including an experimental evaluation, has been presented at IJCAR 2022 41, and as an extended abstract at the DL workshop 2022 42, where it received the best student paper award.
In a joint work with P. Koopmann (TU Dresden), W. DelPinto and R. Schmidt (Univ. Manchester), we are also working on an extended version of an earlier work on abduction in the expressive description logic $\mathrm{\mathcal{A}\mathcal{L}\mathcal{C}}$79.
Proofs for TLA+.
In her PhD work, Rosalie Defourné investigates encodings of the nontemporal theory of TLA+ in the input languages of automated theorem provers for firstorder and higherorder logic, including SMT solvers and Zipperposition. The current SMT backend of the TLA+ Proof System TLAPS heavily relies on simplification techniques such as rewriting and term abstraction in order to transform TLA+ proof obligations into the input language of SMT solvers. Although these techniques are quite powerful, they destroy the structure of the original formulas, and the inherent danger of unsoundness or loss of termination makes it hard to maintain them. The approach proposed in this work consists in axiomatizing TLA+ set theory in the SMT language and in adding suitable triggers that guide the instantiation of quantifiers. It has been validated over an extensive corpus of existing TLA+ proofs, demonstrating that its effectiveness is at least comparable with that of the existing backend, and sometimes outperforms it significantly. Moreover, the addition of trigger annotations cannot invalidate the soundness of the axiomatization, which should help in longerterm maintenance of the proof backend. A paper describing this work has been submitted for publication, and the code is intended to replace the existing SMT backend of TLAPS.
7.2 Formal Methods for Developing and Analyzing Algorithms and Systems
Participants: Étienne André, Johan Arcile, Thomas Bagrel, Martin Bromberger, Horatiu Cirstea, Marie DuflotKremer, Engel EscaffreLefaucheux, Serguei Lenglet, Pierre Lermusiaux, Benjamin Loillier, Dylan Marinho, Dominique Méry, Stephan Merz, PierreEtienne Moreau, Victor Roussanaly, Vincent Trélat, Christoph Weidenbach.
7.2.1 Contributions to Formal Methods of System Design
A complete system of proof rules for auxiliary variables.
A key problem in proving refinement between two specifications of a system at different levels of abstraction is to assign suitable values to internal values of the highlevel specification, given an execution of the lowlevel specification. It is well known that the standard technique of refinement mappings is incomplete; in their classic paper The existence of refinement mappings62, Abadi and Lamport introduced the concept of auxiliary variables and proved the technique to be complete under certain conditions. In joint work with Leslie Lamport (Microsoft Research), we introduce simpler rules for prophecy variables that predict a certain event, as well as rules for combining auxiliary variables. We demonstrate how our rules can be used in a linearizability proof, and prove unrestricted (relative) completeness of our technique. Our paper was published in ACM Transactions on Programming Languages and Systems 17.
Integration of knowledge in formal development.
System engineering advocates a thorough understanding of the engineering domain or certification standards (aeronautics, railway, medical, etc.) associated with the system under design. In this context, engineering domain knowledge plays a predominant role in system design and/or certification, and this knowledge should be made explicit in the corresponding formal design models. Using external theories, we introduce a formal method based on EventB for describing and setting up domainspecific behavioral analyses 49. This method allows us to describe and set up domainspecific behavioral analyses 19. We obtain a formal verification technique for dynamic properties entailed by engineering domain knowledge where EventB formal models are annotated and analyzed in a nonintrusive way, i.e. without destructive alteration. This method is based on the formalization of analyses of behavioral properties relying on domain knowledge as an ontology on the one hand and a metatheory for EventB on the other hand. The proposed method is illustrated using a critical interactive system.
F3FLUID: A formal framework for developing safetycritical interactive systems in FLUID
F3FLUID is developed in the ANR project Formedicis and used for developing safety critical systems. F3FLUID (Formal Framework For FLUID) 19 is a unified formal framework for the development of safetycritical interactive systems. This framework is based on the FLUID (Formal Language of User Interface Design) pivot modeling language defined in the FORMEDICIS project and targeted at expressing highlevel system requirements for interactive systems. This modeling language is specifically designed for handling concepts of safetycritical interactive systems, including domain knowledge. A FLUID model is used as a source model for the generation of several target models in different modeling languages to support the formal verification methods, such as theorem proving and model checking. We use the EventB modeling language for checking functional behaviors, user interactions, safety properties, and domain properties. A FLUID model is transformed into an EventB model, and then the Rodin tool is used to check the internal consistency with respect to the given safety properties. We illustrate the operational semantics of the FLUID language, and the transformation strategy of FLUID models into EventB models, including the tool development. We use the ProB model checker to analyse the temporal properties and to animate the formal specification. In addition, an Interactive Cooperative Objects (ICO) model is derived from the EventB model for animation, visualization and validation of dynamic behaviors, visual properties and task analysis. Finally, an industrial case study, complying with the ARINC 661 standard, MultiPurpose Interactive Applications (MPIA), is used to illustrate the effectiveness of our F3FLUID framework for the development of safetycritical interactive systems.
Modeling hybrid systems by refinement.
Whenever continuous dynamics and discrete control interact, hybrid systems arise. As hybrid systems become ubiquitous and more and more complex, analysis and synthesis techniques are in high demand to design safe hybrid systems. This is however challenging due to the nature of hybrid systems and their designs, and the question of how to formulate and reason about their safety problems. Previous work has demonstrated how to extend the discrete modeling language EventB with support for continuous domains to integrate traditional refinement in hybrid system design. We now propose a strategy that can coherently refine an abstract hybrid system design with safety constraints down to a concrete one, integrated with implementable discrete control, that can behave safely. We demonstrate our proposal on a smart heating system that regulates room temperature between two references.
Certified semantics transformations.
Any given programming language may come with several semantics definitions, such as bigstep, smallstep, or even abstract machines, which can be seen as an implementation of a language. They all describe identical behaviors of programs, but each may be better adapted for some purpose: for instance, smallstep semantics are better suited to prove subject reduction.
To have access to all kinds of semantics at once, we develop transformations between semantics to be able to generate one from the other at no extra cost for the language designer. We propose a transformation from bigstep to smallstep semantics and certify its correctness using Coq certificates: for a given input language in bigstep, we generate the smallstep semantics and a Coq proof script that shows the correspondence between the two semantics 27. We also develop a certified transformation from bigstep to abstract machines 26. Finally, we generate abstract machines in a generic and complete way for nondeterministic languages such as process calculi 33, for which only ad hoc and partial implementations existed so far.
Static analysis of patternfree properties.
From compilation to many approaches of code analysis and formal verification, program transformations are both ubiquitous and critical to properly functioning programs and information systems. In the context of formal verification, it is often necessary to characterize the shape of the result of these transformations. In a typed context, the underlying type system provides syntactic guarantees on the form of these terms by exhibiting, among others, the constructor symbols that they can contain. On the other hand, when performing (program) transformations we often want to eliminate some symbols and, more generally, to ensure that some patterns are absent from the result of the transformation. We have proposed 51 a formalism, based on the notions of patternmatching and rewriting, to express such properties. The proposed approach relies on annotations on function symbols to express set of specifications describing the expected behavior of the associated functions. Using a rewrite system to encode the considered transformation, we introduced a static analysis method to verify that the rewrite system is indeed consistent with the respective annotations, in order to conclude that the transformation actually verifies the given specifications.
Formal verification of an algorithm for computing strongly connected components.
Computing strongly connected components (SCCs) in a graph is a fundamental algorithmic problem that also underlies algorithms for automated system verification by model checking. Stateoftheart algorithms are based on depthfirst search, and they are therefore difficult to parallelize. In his PhD thesis 70, Bloemen introduces a novel variant of Dijkstra's SCC algorithm, together with clever data structures suitable for implementations on multicore architectures. We contributed to ongoing efforts for the formal verification of this algorithm.
During a research project at École des Mines, we formulated a sequential version of the algorithm as two mutually recursive functions in the proof assistant Isabelle/HOL, and we stated suitable pre and postconditions that allowed us to prove the partial correctness of the algorithm. We also proved that the algorithm terminates for finite graphs. The formal proofs have been published in the Archive of Formal Proofs.
In joint work with Jaco van de Pol (University of Aarhus), we also worked on the verification of parallel versions of the algorithm. We represented the algorithm in TLA+ at two different abstraction levels, corresponding to different grains of atomicity, and verified a number of invariants using model checking and the TLAPS proof assistant.
7.2.2 Automated Reasoning Techniques for Verification
Complementary strengths of verification tools for TLA+.
The specification language TLA+ is supported by three main verification tools: the explicitstate model checker TLC, the symbolic SMTbased model checker Apalache, and the interactive proof assistant TLAPS. In joint work with Igor Konnov (Informal Systems) and Markus Kuppe (Microsoft Research), we explore the complementary strengths and weaknesses of these tools, using two specifications of an algorithm for distributed termination detection due to Safra, expressed at two levels of abstraction. Whereas TLC is very easy to use and can be used for verifying properties for small instances of specifications, it suffers from state space explosion. Apalache performs bounded model checking and becomes quite slow when exploring prefixes of executions beyond a handful of transitions due to the growth of the size of SMT constraints. However, it is very useful for checking candidates for inductive invariants where only one transition needs to be considered, and can in that case handle instances with up to 100 active nodes. Finally, TLAPS is not limited by the size of the considered instances, but requires the user to write a proof whose correctness is then checked by the system. The properties of interest include both safety and liveness properties, making good use of the recently added functionality in TLAPS for handling fairness and liveness conditions. Our experience allows us to suggest a methodology for applying the different tools to different aspects of system verification. A paper describing our findings was published at ISOLA 45, and our specifications and proofs are available on GitHub.
Mechanization and Application of SUPERLOG.
In joint work with the groups of Markus Kroetzsch and Christof Fetzer (Technical University of Dresden), we continued the automated reasoning on the so called SUPERLOG (Supervisor Logic) fragment that is meant to provide a basis for formalizing abstract control algorithms found in ECUs (Electronical Control Units). The language comes with support for fully automated verification and also for execution 74. Technically, SUPERLOG is an extension of the (Horn) firstorder BernaysSchoenfinkel fragment with arithmetic constraints. It extends the well known SMT fragment by universally quantified variables. In addition to the already developed sound and complete calculus for the SUPERLOG language and a previously developed Datalog hammer 73, 71 reducing universally as well as existentially quantified queries to plain Datalog, we now refined our hammer by a soft typing discipline. It still outperforms any available stateofthe art technique and improves our previous results by several orders of magnitude. We successfully applied the hammer not only to the ECU scenario but also to a lane change assistant of a car 34. The SUPERLOG language can also be executed by a hierarchic superposition based interpreter. We improved the performance of the interpreter by several order of magnitude as well by providing fast redundancy tests 35.
7.2.3 Timed model checking
Theoretical questions.
In 15, we considered timed games with cost on both transitions and states. Existing work focused mostly on systems where the costs were restricted to nonnegative values, thus failing to represent energy consumption and creation for instance. We showed how to solve these games under some usual restrictions over clocks and resets.
In 12, we considered theoretical problems related to reachability and liveness in (subclasses of) parametric timed automata, exhibiting the frontier between decidability and undecidability.
Heuristics and efficient synthesis.
In 29, 31, we proposed new algorithms using convex merging and zone extrapolations to synthesize parameter valuations in parametric timed automata much more efficiently than in the past. Our algorithms were implemented and demonstrated on a library of benchmarks.
Application to realtime systems.
We developed a tool 28 based on IMITATOR that detects when one can ensure through a simple form of control that a given timed automata is timed opaque (a security property) and which, in the positive case, builds this control.
Monitoring cyberphysical systems.
In 40, we proposed new monitoring algorithms to monitor the (offline or online) behavior of cyberphysical systems used as a black box (no inner information known). We do however add the very rough knowledge of a “bounding model” to eliminate spurious violation detections. Several approaches were proposed with different domains of applications.
In 30, we exemplify a specification by exhibiting concrete examples of sample runs, from a specification given in the form of a quantitative extension of automata, involving realvalued signals.
7.2.4 Model Checking Linear Dynamical Systems
Evolution of simple loops.
Loops are a fundamental staple of any programming language, and the study of loops plays a pivotal role in many subfields of computer science, including automated verification, abstract interpretation, program analysis, semantics, etc. Modeling loops as simple linear dynamical systems, we studied in 44 which kind of properties formulated in Monadic Second Order Logic could be checked over the evolution of a loop. In 32, we parameterized our model, allowing for instance a more accurate representation of the unknown variables that could affect the behavior of a loop. This work aimed at synthesizing for which values of the parameters a loop satisfies some $\omega $regular properties.
Specialization to termination.
Proving the termination of a loop is one of the main properties that one may want to check. In 47 we considered loops (once again modeled as linear dynamical systems) that were already guaranteed to terminate. Despite this guarantee, one could remain within these loops for a very long time. Our result provides a tight bound on the number of iterations within the loop before which the system escapes. We required this bound to be independent of the initial values of the variables (at least when such a bound exists).
Extension to nondeterministic models.
Abstraction of a complex behavior of a system is one of the causes leading to nondeterministic modeling. In 36 we consider the evolution of nondeterministic linear dynamical systems in the form of weighted automata. We establish when and how can we detect whether such systems can diverge, or converge to 0.
7.3 Verification and Analysis of Dynamic Properties of Biological Systems
Participants: Hamid Rahkooy, Thomas Sturm.
7.3.1 Generation and Public Provision of Formal Specifications of Biological Models
In the course of our research line on Biological Systems we are applying automated reasoning to problems such as sustained oscillations and Hopf bifurcations, multistationarity, multiscale model reduction, dynamical invariants, and structural properties of steady state varieties. Compared to numerical analysis and simulation, our approach provides not only quantitative but also qualitative results about network dynamics, to some extent in parametric settings. Our focus has been on reaction networks in the sense of chemical reaction network theory 75. Such networks are usually stored and exchanged in the Systems Biology Markup Language (SBML), a free, open and standardized XMLbased format 78. However, on the one hand, formal methods do not utilize the full information contained in SBML models. For instance, SBML was designed with a focus on network simulation and supports corresponding concepts like events and initial assignments, which are not natural from our point of view. On the other hand, our automated reasoning is based on symbolic computation, which operates on formal objects like polynomials, exact rational numbers, and ordinary differential equations (ODEs), which are not readily available in SBML. For instance, ODEs describing differential network kinetics can be modeled as pieces of code to be used with numerical solvers instead of mathematical expressions accessible for formal methods.
The rigorous construction of of suitable formal models requires joint competence and combined efforts from computer science, mathematics, and biology. Not only resolving but even recognizing issues is a challenge with every single model considered. Software tool chains must be integrated with human interaction. Emerging from combined efforts within the SYMBIONT project (9.1.1), we have picked up the challenge and launched a web service ODEbase (6.2.1) that provides reliable input data for formal methods to the research community. We identify the following benefits:
 Interdisciplinary competence: Researchers get access to biologically adequate translations of existing relevant biomodels instead of ad hoc solutions.
 Availability: ODEbase models used and cited in the literature can be conveniently reviewed on the basis of the original data and reused in followup publications.
 Canonical reference: ODEbase provides an unambiguous mapping of the, in general, too liberal SBML names for species concentrations and parameters to common mathematical notation. This facilitates comparability of results between publications.
 Benchmarking: Beyond its primary purpose, ODEbase is perfectly suited to generate benchmark sets for novel algorithms and software in the field.
At the time of writing, ODEbase comprises 660 models, mostly from the renowned biomodels.net online database 82. For further details on the project see 18.
7.3.2 Approximate Conservation Laws
In Section 3.3 we have seen an example for the reduction of the kinetics of a chemical reaction network to multiple timescales 80. Although general in its implementation, this reduction method can fail in a number of cases. A major cause of failure is the degeneracy of the quasisteady state, when the fast dynamics has a continuous variety of steady states. Typically, this happens when the fast truncated ODEs have first integrals, i.e. quantities that are conserved on any trajectory and that have to be fixed at arbitrary values depending on the initial conditions. The quasisteady states are then no longer hyperbolic, because the Jacobian matrix of the fast part of the dynamics becomes singular. To address this issue, we have now proposed a concept of approximate conservation laws, which allows additional reductions.
Technically, this framework requires parametric versions of various established algorithms from Symbolic Computation. One simple example is the computation of the rank of a matrix with real parameters, which produces a formal finite case distinction where possible ranks are paired with necessary and sufficient conditions as Tarski formulas. This allows to identify critical cases with respect to the abovementioned singularity of the Jacobian. Another example is the use of comprehensive Gröbner bases in the course of parametric computation of certain syzygy modules. From a practical point of view, a central issue with all such algorithms is the combinatorial explosion of the number of cases.
We use SMT solving as well as real quantifier elimination methods to detect inconsistent cases and prune the tree of case distinctions early. The decision procedures used are typically double exponential and can easily turn into a bottleneck preventing termination within reasonable time altogether, in particular when the degrees of polynomial terms get larger. Since the results remain correct also without the elimination of some redundant cases, we combine various methods and use suitable timeouts. This work in progress has led to two preprints so far 54, 55.
8 Bilateral contracts and grants with industry
8.1 Bilateral contracts with industry
Participants: Martin Bromberger, Christoph Weidenbach.
The Max Planck Institute for Informatics (MPIINF) and Logic 4 Business GmbH (L4B) have signed a cooperation contract. Its subject is the application of automated reasoning methods to product complexity management, in particular in the car industry. MPIINF is providing software and knowhow, L4B is providing realworld challenges. The agreement involves Martin Bromberger and Christoph Weidenbach. The company L4B was successfully sold in 2021 to an industrial partner.
9 Partnerships and cooperations
9.1 International initiatives
9.1.1 Participation in other International Programs
ANRNRF ProMiS
Participants: Étienne André, Johan Arcile, Dylan Marinho.

Title:
Provable Mitigation of Side Channel through Parametric Verification

Duration:
2020–2024

Coordinators:
Étienne André, Jun Sun

Partner Institutions:
 University of Lorraine, France (coordinator)
 École Centrale Nantes, France
 Singapore Management University (coordinator)
 Singapore University of Technology and Design

Keywords:
security, formal methods, model checking, timed automata

Summary:
The Spectre vulnerability illustrates the fact that attackers can extract information about private data using a timing attack. It is an example of side channel attacks, where secure information flows through side channels unintentionally. We propose techniques for automatically synthesizing mitigations of side channel attacks using formal verification techniques, by reducing this problem to the parameter synthesis problem of a given formalism. We plan to deliver a fully automated toolkit which can be automatically applied to realworld systems.
 More information:
ANRDFG SYMBIONT
Participants: Hamid Rahkooy, Thomas Sturm.

Title:
Symbolic Methods for Biological Networks

Duration:
July 2018–April 2022

Coordinators:
Thomas Sturm and Andreas Weber/Reinhard Klein

Partner Institutions:
 CNRS / LORIA (coordinator)
 University of Lille 1, France
 University of Montpellier, France
 Inria Saclay Île de France (Lifeware), France
 University of Bonn, Germany (coordinator)
 RWTH Aachen (Department of Mathematics and Joint Research Center for Computational Biomedecine), Germany
 University of Kassel, Germany

Keywords:
molecular interaction networks, computational models, symbolic methods, tropical geometry, real algebraic geometry

Summary:
SYMBIONT is an international interdisciplinary project, funded by ANR in France and by DFG in Germany under the PRCI program. It includes researchers from mathematics, computer science, systems biology, and systems medicine. Computational models in systems biology are built from molecular interaction networks and rate laws, involving parameters, resulting in large systems of differential equations. The statistical estimation of model parameters is computationally expensive and many parameters are not identifiable from experimental data. The project aims at developing novel symbolic methods, aiming at the formal deduction of principal qualitative properties of models, for complementing the currently prevailing numerical approaches. Concrete techniques include tropical geometry, real algebraic geometry, theories of singular perturbations, invariant manifolds, and symmetries of differential systems. The methods are implemented in software and validated against models from computational biology databases.
 More information:
PHC Polonium
Participant: Sergueï Lenglet.

Title:
Abstract Machines for Programming Languages: Investigations in Formal Interderivations

Duration:
2020–2022

Coordinators:
Sergueï Lenglet and Dariusz Biernacki

Partner Institutions:
 University of Lorraine / LORIA, France
 University of Wrocław, Poland

Summary:
The project funds travel of researchers working on the derivation of abstract machines from the formal semantics of programming languages.
9.2 International research visitors
9.2.1 Visits of international scientists
Jaco van de Pol

Status:
professor

Institution of origin:
University of Aarhus

Country:
Denmark

Dates:
1–15 October 2022

Context of the visit:
Collaboration with Étienne André, Dylan Marinho, Stephan Merz

Mobility program/type of mobility:
Invited professor (Université de Lorraine)
9.3 European initiatives
9.3.1 H2020 projects
Matryoshka
Participants: Jasmin Blanchette, Rosalie Defourné, Pascal Fontaine, Stephan Merz, HansJörg Schurr, Sophie Tourret, Uwe Waldmann.
Matryoshka project on cordis.europa.eu

Program:
ERC

Title:
Fast Interactive Verification through Strong HigherOrder Automation

Duration:
March 2017 – February 2022

Partners:
 Free University of Amsterdam, The Netherlands (coordinator)
 Inria
 University of Lorraine, France

Inria contact:
Stephan Merz

Coordinator:
Jasmin Blanchette

Summary:
Proof assistants are increasingly used to verify hardware and software and to formalize mathematics. However, despite some success stories, they remain very laborious to use. The situation has improved with the integration of firstorder automatic theorem provers—superposition provers and SMT (satisfiability modulo theories) solvers—but only so much can be done when viewing automatic provers as black boxes. The purpose of Matryoshka is to deliver much higher levels of automation to users of proof assistants by fusing and extending two lines of research: automatic and interactive theorem proving. Our approach is to enrich superposition and SMT with higherorder reasoning in a careful manner, in order to preserve their desirable properties. With higherorder superposition and higherorder SMT in place, we will develop highly automatic provers building on modern superposition provers and SMT solvers, following a novel stratified architecture, and integrate them in proof assistants. Users stand to experience substantial productivity gains: From 2010 to 2016, the success rate of automatic provers on interactive proof obligations from a representative benchmark suite called Judgment Day has risen from 47% to 77%; with this project, we aim at 90%–95% proof automation.
 More information:
9.3.2 Other European programs
Erasmus+ ARC.

Program:
Erasmus+

Title:
Automated reasoning in the class

Duration:
October 2019 – August 2022

Coordinator:
West University of Timisoara (Romania)

Partners:
 Johannes Kepler University Linz, Austria
 RWTH Aachen, Germany
 Eszterházy Károly Catholic University, Eger, Hungary
 University of Lorraine, France

Inria contact:
Sorin Stratulat

Summary:
The main objective of the project is to improve the education of computer science students in fields related to computational logic, by creating innovative and advanced learning material that uses automated reasoning and by training a large number of academic staff in using this in a modern way. Thus indirectly the project objectives include the effects of increased software reliability: virus elimination, online safety, better detection of negative online phenomena (fake news, cyberbullying, etc.), and other.
COST EuroProofNet.

Program:
COST

Title:
European Research Network on Formal Proofs (COST action CA20111)

Duration:
October 2021 – October 2025

Coordinator:
Inria

Inria contact:
Frédéric Blanqui, Stephan Merz

Team participants:
Pascal Fontaine (WG leader, management committee), Stephan Merz, HansJörg Schurr, Sophie Tourret

Summary:
EuroProofNet is the European research network on digital proofs. EuroProofNet aims at boosting the interoperability and usability of proof systems. The action now gathers about 300 researchers from 40 different countries; it is coordinated by a core group chaired by Frédéric Blanqui. EuroProofNet organizes meetings and schools, and provides grants to its members for shortterm scientific missions in another country.
9.4 National initiatives
ANR Project BLaSST

Title:
Enhancing B Language Reasoners Using SAT and SMT Techniques

Duration:
March 2022 – February 2026

Coordinator:
Stephan Merz

Partner Institutions:
 Inria Nancy (coordinator)
 University of Artois & CRIL, Lens
 CLEARSY, AixenProvence
 University of Liège, Belgium

Team participants:
Pascal Fontaine, Stephan Merz, Sophie Tourret

Summary:
The BLaSST project targets bridging combinatorial and symbolic techniques in automatic theorem proving, in particular for proof obligations generated from B models. It focuses on advancing the state of the art in automated reasoning, in particular SAT and SMT techniques, and on making these techniques available to software verification. More specifically, encoding techniques, optimized resolution techniques, model generation, and lemma suggestion will be investigated. The expected scientific impact is a substantially higher degree of automation of solvers for expressive input languages by leveraging higherorder reasoning and enumerative instantiations over finite domains, as well as useful feedback for verification conditions that cannot be proved. The effectiveness of the techniques developed in the project will be quantified by applying them to benchmark sets provided by the industrial partner. The industrial impact of BLaSST will be a higher productivity of proof engineers. The collections of benchmarks and the reasoning engines will be made openly available under permissive opensource licenses.

Keywords:
B method, deductive verification, SAT, SMT, higherorder logic
 More information:
ANR Project DISCONT

Title:
Correct integration of discrete and continuous models

Duration:
March 2018 – September 2023

Coordinator:
Dominique Méry

Partner Institutions:
 University of Lorraine (coordinator)
 ENSEEIHT & IRIT, Toulouse
 University Paris Est & LACL, Créteil
 CLEARSY, AixenProvence

Team participants:
Zheng Cheng, Dominique Méry

Summary:
CyberPhysical Systems (CPSs) connect the real world to software systems through a network of sensors and actuators that interact in complex ways, depending on context and involving different spatial and temporal scales. Typically, a discrete software controller interacts with its physical environment in a closedloop schema where input from sensors is processed and output is generated and communicated to actuators. We are concerned with the verification of the correctness of such discrete controllers, which requires correct integration of discrete and continuous models. Correctness should arise from a design process based on sound abstractions and models of the relevant physical laws. The systems are generally characterized by differential equations with solutions in continuous domains; discretization steps are therefore of particular importance for assessing the correctness of CPSs. DISCONT aims at bridging the gap between the discrete and continuous worlds of formal methods and control theory. We will lift the level of abstraction above that found in current bridging techniques and provide associated methodologies and tools. Our concrete objectives are to develop a formal hybrid model, elaborate refinement steps for control requirements, propose a rational stepwise design method and support tools, and validate them based on use cases from a range of application domains.

Keywords:
cyberphysical systems, discrete models, continuous models, refinement, verification, tools
 More information:
ANR Project EBRP

Title:
Enhancing EventB and RODIN: EventBRodinPlus

Duration:
January 2020 – January 2024

Coordinator:
Dominique Méry

Partner Institutions:
 INPTENSEEIHT & IRIT, Toulouse
 CentraleSupelec & LRI
 University of Lorraine & LORIA
 University ParisEst Créteil & LACL
 University of Düsseldorf, Germany
 University of Southampton, School of Electronics and Computer Science, United Kingdom

Team participants:
Zheng Cheng, Dominique Méry, Guillaume Verdier

Keywords:
formal IDE, theory, proof managementr, cyberphysical systems, discrete models, continuous models, refinement, verification, tools

Summary:
The purpose of EBRP is to enhance EventB and the corresponding Rodin toolset. This will be done by engaging in some basic research dealing with various mathematical theories that are not currently available in EventB and Rodin. The development of complex systems usually involves different scientific disciplines and skills. For instance, modeling behaviors and interactions of autonomous systems may require concepts from control theory such as differential equations, communication protocols, resource allocation, access control rules, etc. EBRP targets the definition of extension mechanisms for EventB rather than defining domainspecific modeling languages, and implementing those mechanisms within Rodin.
 More information:
ANR Project Formedicis

Title:
Formal methods for the development and the engineering of critical interactive systems

Duration:
January 2017 – July 2022

Coordinator:
David Chemouil

Partner Institutions:
 ONERA, Toulouse (coordinator)
 ENSEEIHT & IRIT, Toulouse
 ENAC, Toulouse
 University of Lorraine

Team participants:
Horatiu Cirstea, Dominique Méry

Summary:
During the last 30 years, the aerospace domain has successfully devised rigorous methods and tools for the development of safe functionallycorrect software. During this process, interactive software has received a relatively lower amount of attention. However, HumanSystem Interactions (HSI) are important for critical systems and especially in aeronautics: for example, the investigation into the crash of the RioParis flight AF 447 in 2009 pointed out a design issue in the Flight Director interface as one of the original causes of the crash. Formedicis aims at designing a formal hub language, in which designers can express their requirements concerning the interactive behavior that must be embedded inside applications, and at developing a framework for validating, verifying, and implementing critical interactive applications expressed in that language.

Keywords:
critical systems, aeronautics, humansystem interaction, system requirements
ANR Project ICSPA

Title:
Interoperable and Confident Setbased Proof Assistants

Duration:
January 2022 – December 2025

Coordinator:
Catherine Dubois

Partner Institutions:
 ENSIIE & Samovar, Évry
 Inria (Nancy and Saclay research centers)
 University Paul Sabatier & IRIT, Toulouse
 University of Montpellier & LIRMM, Montpellier
 CLEARSY, AixenProvence

Team participants:
Dominique Méry, Stephan Merz

Summary:
The B, EventB, and TLA+ formal methods are based on different flavors of set theory. The ICSPA project aims at formally relating these different theories for allowing users (i) to independently certify proofs carried out using the automatic proof tools developed for these formal methods and (ii) to transfer developments, including their proofs, carried out in one of these languages to another one. The objectives are to reinforce confidence in developments carried out using these methods and to enable interoperability between them. The foundation for achieving these goals lies in the encoding of the set theories in the Dedukti logical framework developed at Inria Saclay, which implements the $\lambda \Pi $calculus modulo theory.

Keywords:
B method, TLA+, set theory, logical framework
 More information:
DFG Transregional Research Center 248 CPEC

Title:
Foundations of Perspicuous Software Systems.

Duration:
January 2019 – December 2022.

Coordinators:
Holger Hermanns and Raimund Dachselt

Partner Institutions:
 Saarland University (coordinator)
 University of Dresden (coordinator)
 Max Planck Institute for Software Systems, Saarbrücken

Team participants:
Fajar Haifani, Sophie Tourret, Christoph Weidenbach.

Summary:
With cyberphysical technology increasingly impacting our lives, it is very important to ensure that humans can understand them. Systems lack support for making their behavior plausible to their users. And even for technology experts it is nowadays virtually impossible to provide scientifically wellfounded answers to questions about the exact reasons that lead to a particular decision, or about the responsibility for a malfunctioning. The root cause of the problem is that contemporary systems do not have any builtin concepts to explicate their behavior. They calculate and propagate outcomes of computations, but are not designed to provide explanations. They are not perspicuous. The key to enable comprehension in a cyberphysical world is a science of perspicuous computing.

Keywords:
cyberphysical system, explainability, causal analysis
 More information:
9.5 Regional initiatives
The PhD thesis of Rosalie Defourné is partly funded by Région Grand Est.
10 Dissemination
10.1 Promoting scientific activities
10.1.1 Scientific events: organisation
General chair, scientific chair.
Dominique Méry was cochair of the conferences MEMOCODE and ABZ.
Member of organizing committees.
Sophie Tourret was workshop cochair of the conference IJCAR (International Joint Conference on Automated Reasoning).
10.1.2 Scientific events: selection
Chair of conference program committees.
Jasmin Blanchette was cochair of the program committee of the conference IJCAR (International Joint Conference on Automated Reasoning).
Member of conference program committees.
 Étienne André: FASE (25th International Conference on Fundamental Approaches to Software Engineering), FORTE (42nd International Conference on Formal Techniques for Distributed Objects, Components, and Systems), FTSCS (8th International Workshop on Formal Techniques for SafetyCritical Systems), ICFEM (23rd International Conference on Formal Engineering Methods), PRDC (27th IEEE Pacific Rim International Symposium on Dependable Computing), TASE (16th Theoretical Aspects of Software Engineering Conference).
 Jasmin Blanchette: ITP (Interactive Theorem Proving), TACAS (Tools and Algorithms for the Construction and Analysis of Systems).
 Horatiu Cirstea: FSCD (7th International Conference on Formal Structures for Computation and Deduction, RuleML+RR (6th International Joint Conference on Rules and Reasoning), TASE (International Symposium on Theoretical Aspects of Software Engineering).
 Pascal Fontaine: IJCAI (31st International Joint Conference on Artificial Intelligence), IJCAR (International Joint Conference on Automated Reasoning).
 Sergueï Lenglet: ICE (15th Interaction and Concurrency Experience).
 Dominique Méry: FIDE (7th Workshop on Formal Integrated Development Environment), SETTA (Symposium on Dependable Software Engineering: Theories, Tools and Applications), MEDI (11th International Conference on Model and Data Engineering), FMAS (Fourth Workshop on Formal Methods for Autonomous Systems), ICFEM (23rd International Conference on Formal Engineering Methods), ICI2ST (3rd International Conference on Information Systems and Software Technologies), TASE (International Symposium on Theoretical Aspects of Software Engineering).
 Stephan Merz: ICFEM (23rd International Conference on Formal Engineering Methods), iFM (17th International Conference on integrated Formal Methods), ARNQL (4th International Workshop on Automated Reasoning in Quantified NonClassical Logics), FIDE (7th Workshop on Formal Integrated Development Environments).
 Sorin Stratulat: SYNASC (24th International Symposium on Symbolic and Numeric Algorithms for Scientific Computing), ICEUTE (13th International Conference on EUropean Transnational Educational), CISIS (15th International Conference on Computational Intelligence in Security for Information Systems).
 Thomas Sturm: CASC (24th International Workshop on Computer Algebra in Scientific Computing).
 Sophie Tourret: IJCAI (31st International Joint Conference on Artificial Intelligence) and IJCAR (11th International Joint Conference on Automated Reasoning).
 Uwe Waldmann: IJCAR (11th International Joint Conference on Automated Reasoning).
 Christoph Weidenbach: IJCAR 2022 (11th International Joint Conference on Automated Reasoning).
10.1.3 Journal
Member of editorial boards.
 Jasmin Blanchette is editorinchief of the Journal of Automated Reasoning.
 Dominique Méry is a member of the editorial boards of the journals Formal Aspects of Computing and Science of Computer Programming.
 Thomas Sturm is an editor of the Journal of Symbolic Computation and of Mathematics in Computer Science.
 Christoph Weidenbach is an editor of the Journal of Automated Reasoning.
Special issues edited.
 Thomas Sturm has edited a special issue of the Springer journal Mathematics in Computer Science on Computer Algebra in Scientific Computing50.
10.1.4 Invited talks
 Stephan Merz gave an invited tutorial on the TLA+ language and its support tools at the University of Lancaster and an invited presentation on auxiliary variables at the CISPALORIA workshop in Nancy.
 Thomas Sturm gave an invited talk on Real Quantifier Elimination by Virtual Substitution at a workshop on Trends in Arithmetic Theories at ICALP 2022 (49th EATCS International Colloquium on Automata, Languages, and Programming).
 Christoph Weidenbach gave an invited talk on Algorithm Design for Hard Problems at the university of New Mexico.
10.1.5 Leadership within the scientific community
 Pascal Fontaine is an elected CADE Trustee. In the COST action EuroProofNet, he was workgroup leader until October 2022, he is now workgroup viceleader, and he is in the management committee as one Belgian representative. He was member of the committees for the William McCune PhD Award 2022, and for the Herbrand Award 2022.
 Dominique Méry is a member of the IFIP Working Group 1.3 on Foundations of System Specifications.
 Stephan Merz is a member of the IFIP Working Group 2.2 on Formal Description of Programming Concepts.
 Sophie Tourret has become an elected CADE Trustee in 2022.
 Christoph Weidenbach was an elected CADE Trustee and president of CADE until September 2022.
10.1.6 Scientific expertise
 Stephan Merz reviewed a Wittgenstein project for the Austrian Science Fund (FWF) and two ERC project proposals.
 Thomas Sturm is a project partner in the Engineering and Physical Sciences Research Council (EPSRC) Projects EP/T015748/1 and EP/T015713/1Pushing Back the DoublyExponential Wall of Cylindrical Algebraic Decomposition, Universities of Coventry and Bath, UK.
10.1.7 Research administration
 Étienne André has been involved in three initiatives around open research
data:
 He has been a member since 2021 of the “EOSC (European Open Science Cloud) Future User Group”, that aims to prepare the opening of the EOSC platform, aiming (among many other goals) at opening the European scientists research data.
 He has been a member since 2022 of the national board of the disciplinary DoRANum, aiming at helping Francebased scientists in opening their research data. This participation notably leads him to prepare pedagogical material specifically dedicated to researchers in computer science, to help them to open their research data.
 He has been a member of the network of data ambassadors at University of Lorraine since its creation in 2020. The goal of this network is to help researchers within University of Lorraine to open their data when possible, and keep them closed when necessary.
 Étienne André and Marie DuflotKremer were members of a hiring committee for an assistant professor position at IBISC, Évry.
 Stephan Merz is a member of the executive committee of the project on citizens' trust in the digital world (DigiTrust) funded by Lorraine Université d'Excellence.
 Sophie Tourret was a jury member for the CRCN researchers recruitment campaign 2022 at Inria Nancy  Grand Est.
10.2 Teaching  Supervision  Juries
10.2.1 Teaching
 BUT 1: Étienne André, Data structures, 42 HETD, Université de Lorraine – IUT Charlemagne, France.
 BUT 1: Étienne André, Humanmachine interfaces, 57 HETD, Université de Lorraine – IUT Charlemagne, France.
 BUT 1: Étienne André, Architecture des réseaux, 32 HETD, Université de Lorraine – IUT Charlemagne, France.
 BUT 1: Étienne André, Objectoriented software design, 38 HETD, Université de Lorraine – IUT Charlemagne, France.
 BUT 2: Étienne André, Supervised projects, 56 HETD, Université de Lorraine – IUT Charlemagne, France.
 Master: Horatiu Cirstea, Advanced software engineering, 40 HETD, M2 Informatique, Université de Lorraine, France.
 Master: Horatiu Cirstea, Software engineering & Design patterns, 80 HETD, M1 informatique, Université de Lorraine, France.
 Master: Horatiu Cirstea, Software engineering, 40 HETD, 2A ENSEM, Université de Lorraine, France.
 Licence: Horatiu Cirstea, Algorithms and programming 3, 60 HETD, L2, Université de Lorraine, France.
 Licence: Marie DuflotKremer, Algorithms and programming 1, 60 HETD, L1, Université de Lorraine, France.
 Diplôme inter universitaire: Marie DuflotKremer, formation d'enseignants du secondaire à la spécialité NSI, 18 HETD, Université de Lorraine, France.
 Licence: Marie DuflotKremer, Individual support for algorithms and programming, 60 HETD, L1, Université de Lorraine, France.
 Master: Marie DuflotKremer, Using unplugged activities for future teachers.
 Master: Marie DuflotKremer and Stephan Merz, Elements of model checking, 24 HETD, M2 Informatique, Université de Lorraine, France.
 Master: Marie DuflotKremer and Stephan Merz, Distributed algorithms, 30 HETD, M1 Informatique, Université de Lorraine, France.
 Licence: Engel EscaffreLefaucheux, Objectedoriented programming, 14 HETD, L2, Université de Lorraine.
 Classe préparatoire universitaire: Engel EscaffreLefaucheux, Algorithms and programming (2 and 3), 15 HETD, Université de Lorraine.
 Licence: Engel EscaffreLefaucheux, Algorithms and programming 2, 20 HETD, L2, Université de Lorraine.
 Master: Engel EscaffreLefaucheux, supervision of 3 students in an intial research experience, M1, Université de Lorraine.
 BUT 1: Sergueï Lenglet, Introduction to data bases, 110 HETD, Université de Lorraine – IUT Charlemagne, France.
 BUT 1: Sergueï Lenglet, Use of data bases, 60 HETD, Université de Lorraine – IUT Charlemagne, France.
 BUT 2: Sergueï Lenglet, Functional programming, 24 HETD, Université de Lorraine – IUT Charlemagne, France.
 Master: Dominique Méry, Formal Modeling for Softwarebased Systems 40 HETD, M2 Informatique, Université de Lorraine, France.
 Master: Dominique Méry, Models and algorithms, M1 Telecom Nancy, 48 HETD, Université de Lorraine, France.
 Master: Dominique Méry, Formal Modeling for Softwarebased Systems, M2 Telecom Nancy, 24 HETD, Université de Lorraine, France.
 Master: Sophie Tourret, Decision Procedures for Program Verification, 32 HETD, M2 Informatique and Master Erasmus Mundus DESEM (academic year 20212022), Université de Lorraine, France.
 Master: Sophie Tourret, Decision Procedures for Program Verification, M2 Informatique (academic year 20222023), Université de Lorraine, France.
 Master: Sophie Tourret and Stephan Merz, Secure Coding, M1 Mines Nancy, 26 HETD, Université de Lorraine, France
 Master: Uwe Waldmann, Automated Reasoning I, 60 HETD, Universität des Saarlandes, Germany.
 Master: Uwe Waldmann and Christoph Weidenbach, Automated Reasoning II, 40 HETD, Universität des Saarlandes, Germany.
 Licence: Markus Bläser, Karl Bringmann, Martin Bromberger, and Christoph Weidenbach, Competitive Programming, 40 HETD, Universität des Saarlandes, Germany.
 Master: Sorin Stratulat, Software design, 30 HETD, M2 Informatique, Université de Lorraine, France.
 Licence: Sorin Stratulat, Algorithms and programming, 105 HETD, L1 Informatique, Université de Lorraine, France.
 Licence: Sorin Stratulat, Logic for computer science, 26 HETD, L1 Informatique, Université de Lorraine, France.
 Licence: Victor Roussanaly, Data bases, L3 Polytech Nancy, 60 HETD, Université de Lorraine, France.
 Licence: Victor Roussanaly, Objectoriented programming, L3 Polytech Nancy, 42 HETD, Université de Lorraine, France.
 Master: Victor Roussanaly, Introduction to cryptography, M2 Polytech Nancy, 15 HETD, Université de Lorraine, France.
10.2.2 Supervision
 PhD: Guillaume Ambal, Skeletal Semantics Transformations, Université de Rennes 1. Supervised by Alan Schmitt and Sergueï Lenglet, 18 October 2022.
 PhD: Pierre Lermusiaux, Static analysis of pattern eliminating transformations, Université de Lorraine. Supervised by Horatiu Cirstea and PierreÉtienne Moreau, 8 September 2022.
 PhD: Christoph Lüders, Algorithmic Reduction of Biochemical Reaction Networks, University of Kassel, Germany. Supervised by Werner Seiler, Thomas Sturm, Sebastian Walcher, Andreas Weber, 2 June 2022.
 PhD: HansJörg Schurr, Stronger SMT Solvers for Proof Assistants: Proofs, Quantifier Simplification, Strategy Schedules, Université de Lorraine. Supervised by Jasmin Blanchette, Pascal Fontaine, and Stephan Merz, 7 October 2022.
 PhD in progress: Thomas Bagrel, Type systems for memory safety in functional programming languages, Université de Lorraine (CIFRE with Tweag company). Supervised by Horatiu Cirstea, since April 2022.
 PhD in progress: Rosalie Defourné, SMT for TLAPS, Université de Lorraine. Supervised by Jasmin Blanchette, Pascal Fontaine, and Stephan Merz, since March 2019.
 PhD: Martin Desharnais, Verification in Isabelle/HOL of automated reasoning results, MPI for Informatics, Saarland University, Sarrebruck, Allemagne. Supervised by Jasmin Blanchette, Sophie Tourret and Christoph Weidenbach, since August 2021.
 PhD: Fajar Haifani, On a Notion of Abduction and Relevance for FirstOrder Logic Clause Sets, MPI for Informatics, Saarland University, Sarrebruck, Allemagne. Supervised by Sophie Tourret and Christoph Weidenbach, since November 2019.
 PhD in progress: Hendrik Leidinger, SCL in FirstOrder Logic with Equality, Universität des Saarlandes. Supervised by Christoph Weidenbach, since August 2020.
 PhD in progress: Lorenz Leutgeb, Reasoning with SCL, Universität des Saarlandes. Supervised by Christoph Weidenbach, since October 2021.
 PhD in progress: Dylan Marinho, Detecting timing attacks using formal methods, Université de Lorraine. Supervised by Étienne André, since October 2020.
 PhD in progress: Simon Schwarz, Automatic Reasoning for Security, Universität des Saarlandes. Supervised by Christoph Weidenbach, since October 2022.
 L3: Florent Krasnopol, Verifying in Isabelle/HOL a notion of consequence relation, ENS Paris Saclay, summer internship. Supervised by Sophie Tourret, JuneJuly 2022.
 M2: Shapagat Bolat, Enforcing timeopacity of timed automata, Master internship for Université de Lorraine, MarchJune 2022, supervised by Étienne André and Engel Lefaucheux
 M2: Nurgul Osmonova, Optimising Diagnosability in probabilistic systems, Master internship for Université de Lorraine, MarchJune 2022, supervised by Engel Lefaucheux.
 M1: Vincent Trélat, A mechanized proof of an algorithm for computing strongly connected components in a graph, research project at École des Mines de Nancy, September 2021July 2022, supervised by Stephan Merz.
 M2: Zunaira Zaman, Distributed PlusCal, Master internship for Université de Lorraine, MarchJune 2022, supervised by Horatiu Cirstea and Stephan Merz.
10.2.3 Juries
 Étienne André reviewed the PhD thesis of Bastien Serée (Nantes) and was a PhD jury member of the defense of Mathieu Hilaire (Saclay).
 Stephan Merz was a reviewer of the PhD theses of Benjamin Binder (Saclay) and of Pierre Civit (Paris). He was the president of the PhD committees of Aurèle Barrière (Rennes), Abir Laraba (Nancy), and Matthieu Nicolas (Nancy).
10.3 Popularization
10.3.1 Internal or external Inria responsibilities
 Marie DuflotKremer is the deputy vicepresident for outreach activities in the supervisory council of SIF (Société Informatique de France) and a member of the scientific committee of Fondation Blaise Pascal, which supports projects on popularization activities.
 Marie DuflotKremer is a member of the jury of the Cyber Agora 41 award organized by ANSSI (the French agency for the security of information systems) for rewarding a novel related to computer science or cybersecurity.
 Marie DuflotKremer is a member of the jury of CAPES NSI, the French hiring exam for becoming a computer science teacher in secondary schools.
 Marie DuflotKremer is a member of the Interstices editorial board, a Web site launched by Inria that publishes popularization articles.
 Christoph Weidenbach is the head of the steering committee of the German Computer Science Competition for High School Students (BWINF) and a coorganizer and the president of the jury of the final round that took place in Berlin in September 2022. Stephan Merz was a member of that jury.
10.3.2 Articles and contents
 Within a SIF working group, Marie DuflotKremer supervised the production of four videos on the four basic blocks of computer science: machines, languages, data, and algorithms.
10.3.3 Interventions
 Marie DuflotKremer organized a workshop on databases and gave a short talk at the Journée NSISNT in April in Nancy.
 Marie DuflotKremer was an invited speaker at the 6th Journée académique sur l'enseignement de l'informatique in Marseille in May 2022.
 Marie DuflotKremer gave a presentation “Rencontre avec une informagicienne” in Strasbourg in June 2022.
 Marie DuflotKremer organized a workshop on unplugged computer science activities in Strasbourg in October 2022.
 Marie DuflotKremer and Sophie Tourret organized a stand at the “Fête de la science” event (October 2022), to present unplugged computer science activities to the general public with the help of bachelor and master students.
 Marie DuflotKremer and Sophie Tourret organized an outreach activity around the game “Turing tumble” (a mechanical, marblepowered programmable computer) at the Ludothèque SaintNicolas in Nancy in November 2022.
 Marie DuflotKremer and Sophie Tourret took part in several meetings with primary and secondary school students to present computer science and research within the Chiche program.
11 Scientific production
11.1 Major publications
 1 inproceedingsveriT: an open, trustable and efficient SMTsolver.Proc. Conference on Automated Deduction (CADE)5663Lecture Notes in Computer ScienceMontreal, CanadaSpringer2009, 151156
 2 articleA complete and terminating approach to linear integer solving.Journal of Symbolic Computation100September 2020, 102136
 3 incollectionThe EventB Modelling Method  Concepts and Case Studies.Logics of Specification LanguagesMonographs in Theoretical Computer ScienceSpringerFebruary 2008, 33140
 4 inproceedingsTLA+ Proofs.18th International Symposium On Formal Methods  FM 20127436Lecture Notes in Computer ScienceParis, FranceSpringer2012, 147154
 5 articleRedlog: Computer algebra meets computer logic.ACM SIGSAM Bull.3121997, 29
 6 articleDetection of Hopf bifurcations in chemical reaction networks using convex coordinates.Journal of Computational Physics291March 2015, 279  302
 7 articleSuperposition Decides the FirstOrder Logic Fragment Over Ground Theories.Mathematics in Computer Science642012, 427456
 8 incollectionThe Specification Language TLA+.Logics of specification languagesMonographs in Theoretical Computer ScienceSpringer2008, 401452
 9 inproceedingsVerification and synthesis using real quantifier elimination.Proc. ISSAC 2011San Jose, United StatesACM PressJune 2011, 329
 10 inproceedingsSPASS Version 3.5.22nd International Conference on Automated Deduction (CADE22)5663LNAIMontreal, CanadaSpringer2009, 140145
11.2 Publications of the year
International journals
 11 articleGuaranteeing Timed Opacity using Parametric Timed Model Checking.ACM Transactions on Software Engineering and Methodology314October 2022, 136
 12 articleReachability and liveness in parametric timed automata.Logical Methods in Computer Science181February 2022
 13 articleTimed automata as a formalism for expressing security: A survey on theory and practice.ACM Computing SurveysJune 2022
 14 articleThe central role of data repositories and data models in Data Science and Advanced Analytics.Future Generation Computer Systems129April 2022, 1317
 15 articleOneClock Priced Timed Games with Arbitrary Weights.Logical Methods in Computer Science183August 2022, 51
 16 articleAutomated Reasoning in the Class.ComputerAlgebraRundbrief71October 2022, 2126
 17 articleProphecy Made Simple.ACM Transactions on Programming Languages and Systems (TOPLAS)442June 2022, 127
 18 articleODEbase: A Repository of ODE Systems for Systems Biology.Bioinformatics Advances21April 2022
 19 articleFormal domaindriven system development in EventB: Application to interactive critical systems.Journal of Systems Architecture135February 2023, 102798
 20 articleSelected papers from The 13th International Symposium on Theoretical Aspects of Software Engineering 29 July – 1 August 2019, Guilin, China.Science of Computer Programming218June 2022, 102804
 21 articleSelected papers from the Rigorous StateBased Methods 7th International Conference, ABZ 2020, Ulm, Germany, May 27–29, 2020.Science of Computer Programming216April 2022, 102780
 22 articlePolite Combination of Algebraic Datatypes.Journal of Automated Reasoning663August 2022, 331355
 23 articleMaking HigherOrder Superposition Work.Journal of Automated Reasoning664November 2022, 541564
 24 articleExtending a brainiac prover to lambdafree higherorder logic.International Journal on Software Tools for Technology Transfer241February 2022, 6787
 25 articleA Comprehensive Framework for Saturation Theorem Proving.Journal of Automated Reasoning664November 2022, 499539
International peerreviewed conferences
 26 inproceedingsCertified Abstract Machines for Skeletal Semantics.CPP 2022  11th ACM SIGPLAN International Conference on Certified Programs and ProofsPhiladelphia, United StatesJanuary 2022, 113
 27 inproceedingsCertified Derivation of SmallStep From BigStep Skeletal Semantics.PPDP 2022  24th International Symposium on Principles and Practice of Declarative ProgrammingTbilisi, GeorgiaSeptember 2022, 148
 28 inproceedingsstrategFTO: Untimed control for timed opacity.Proceedings of the 8th International Workshop on Formal Techniques for SafetyCritical Systems (FTSCS 2022)8th International Workshop on Formal Techniques for SafetyCritical Systems (FTSCS 2022)Proceedings of the 8th International Workshop on Formal Techniques for SafetyCritical Systems (FTSCS 2022)Auckland, New ZealandACMDecember 2022, 2733
 29 inproceedingsEfficient Convex Zone Merging in Parametric Timed Automata.20th International Conference on Formal Modeling and Analysis of Timed Systems13465Lecture Notes in Computer ScienceWarsaw, PolandSpringer International PublishingAugust 2022, 200218
 30 inproceedingsExemplifying Parametric Timed Specifications over Signals with Bounded Behavior.Proceedings of the 14th NASA Formal Methods Symposium (NFM 2022)14th NASA Formal Methods Symposium (NFM 2022)13260Lecture Notes in Computer SciencePasadena, United StatesSpringer International PublishingMay 2022, 470488
 31 inproceedingsZone Extrapolations in Parametric Timed Automata.Proceedings of the 14th NASA Formal Methods Symposium (NFM 2022)14th NASA Formal Methods Symposium (NFM 2022)13260Lecture Notes in Computer ScienceCaltech, Pasadena, United StatesSpringer International PublishingMay 2022, 451469
 32 inproceedingsParameter Synthesis for Parametric Probabilistic Dynamical Systems and PrefixIndependent Specifications.33rd International Conference on Concurrency Theory (CONCUR 2022)Varsovie, PolandSeptember 2022
 33 inproceedingsNonDeterministic Abstract Machines.CONCUR 2022  33rd International Conference on Concurrency TheoryVarsovie, PolandSeptember 2022, 124
 34 inproceedingsA Sorted Datalog Hammer for Supervisor Verification Conditions Modulo Simple Linear Arithmetic.Tools and Algorithms for the Construction and Analysis of Systems  28th International Conference, TACAS 202213243Lecture Notes in Computer ScienceMunich (Germany), GermanySpringer International PublishingMarch 2022, 480501
 35 inproceedingsAn Efficient Subsumption Test Pipeline for BS(LRA) Clauses.IJCAR 2022  International Joint Conference in Automated Reasoning13385Lecture Notes in Computer ScienceHaifa, IsraelSpringer International PublishingAugust 2022, 147168
 36 inproceedingsThe boundedness and zero isolation problems for weighted automata over nonnegative rationals.LICS 2022  37th Annual ACM/IEEE Symposium on Logic in Computer ScienceHaifa, IsraelAugust 2022
 37 inproceedingsSeventeen Provers under the Hammer.13th International Conference on Interactive Theorem Proving  ITP 2022Tel Aviv, IsraelJuly 2022
 38 inproceedingsExperiments with Automated Reasoning in the Class.CICM 2022  15th Conference on Intelligent Computer Mathematics13467Lecture Notes in Computer ScienceTbilisi / Hybrid, GeorgiaSpringer International PublishingSeptember 2022, 287304
 39 inproceedingsARC: An Educational Project on Automated Reasoning in the Class.EdMedia + Innovate Learning 2022  AACE ConferencesNew York, United StatesJune 2022
 40 inproceedingsOffline and Online Monitoring of Scattered Uncertain Logs Using Uncertain Linear Dynamical Systems.42nd International Conference on Formal Techniques for Distributed Objects, Components, and Systems13273Lecture Notes in Computer ScienceLucca, ItalySpringer International PublishingJune 2022, 6787
 41 inproceedingsConnectionMinimal Abduction in EL via Translation to FOL.LNCS, LNAI, IJCARAutomated Reasoning13385Lecture Notes in Computer ScienceHaifa, IsraelSpringer International Publishing; Springer International PublishingAugust 2022, 188207
 42 inproceedingsConnectionMinimal Abduction in EL via Translation to FOL: Extended Abstract.CEUR Workshops proceedings35th International Workshop on Description Logics (DL 2022)Haifa, IsraelAugust 2022
 43 inproceedingsSemantic Relevance.IJCAR, International Joint Conference in Automated Reasoning13385Lecture Notes in Computer ScienceHaifa, IsraelSpringer International PublishingAugust 2022, 208227
 44 inproceedingsWhat’s decidable about linear loops?Proceedings of the ACM on Programming Languages49th ACM SIGPLAN Symposium on Principles of Programming Languages (POPL 2022)6POPL 2022Philadelphia, United StatesJanuary 2022, 1  25
 45 inproceedingsSpecification and Verification with the TLA+ Trifecta: TLC, Apalache, and TLAPS.Leveraging Applications of Formal Methods, Verification and Validation. 11th International Symposium, ISoLA 202213701Lecture Notes in Computer ScienceRhodes, GreeceSpringer International PublishingOctober 2022, 88105
 46 inproceedingsSCL(EQ): SCL for FirstOrder Logic with Equality.IJCAR, International Joint Conference in Automated Reasoning13385Lecture Notes in Computer ScienceHaifa, IsraelSpringer International PublishingAugust 2022, 228247
 47 inproceedingsBounding the Escape Time of a Linear Dynamical System over a Compact Semialgebraic Set.47th International Symposium on Mathematical Foundations of Computer Science (MFCS 2022)24147th International Symposium on Mathematical Foundations of Computer ScienceVienna, Austria2022, 14
Conferences without proceedings
 48 inproceedingsF5: A REDUCE Package for Signaturebased Gröbner Basis Computation.CASC 2022  Computer Algebra in Scientific ComputingGezbe, Turkey2022
Scientific book chapters
 49 inbookEmpowering the EventB Method Using External Theories.13274Integrated Formal MethodsLecture Notes in Computer ScienceSpringer International PublishingJune 2022, 1835
Edition (books, proceedings, special issue of a journal)
 50 periodicalSpecial Issue on Computer Algebra in Scientific Computing (CASC 2021).Mathematics in Computer Science16September 2022
Doctoral dissertations and habilitation theses
 51 thesisStatic analysis of pattern eliminating transformations.Université de Lorraine (UL)September 2022
 52 thesisStronger SMT Solvers for Proof Assistants : Proofs, Quantifier Simplification, Strategy Schedules.Université de LorraineOctober 2022
Reports & preprints
 53 reportNonDeterministic Abstract Machines.RR9475InriaJuly 2022, 133
 54 miscA Computational Approach to Complete Exact and Approximate Conservation Laws of Chemical Reaction Networks.December 2022
 55 miscReduction of Chemical Reaction Networks with Approximate Conservation Laws.December 2022
 56 miscModel Checking Linear Dynamical Systems under Floatingpoint Rounding.November 2022
 57 reportActivity for learning computational thinking in plugged and unplugged mode.006UCA  INSPE Académie de NiceOctober 2022
Other scientific publications
 58 articleForeword.Mathematics in Computer Science1623September 2022, 16
11.3 Other
Scientific popularization
 59 articleRécurrence noethérienne pour le raisonnement de premier ordre.1024 : Bulletin de la Société Informatique de France19April 2022, 157169
 60 articleA Posthumous Contribution by Larry Wos: Excerpts from an Unpublished Column.Journal of Automated Reasoning664November 2022, 575584
11.4 Cited publications
 61 articleEfficiency and completeness of the set of support strategy in theorem proving.Journal of the ACM1241965, 536541
 62 articleThe Existence of Refinement Mappings.Theoretical Computer Science812May 1991, 253284
 63 bookModeling in EventB: System and Software Engineering.Cambridge University Press2010
 64 inproceedingsParametric realtime reasoning.Proc. 25th Annual ACM Symp. Theory of ComputingSan Diego, CA, USAACM1993, 592601
 65 inproceedingsIMITATOR 3: Synthesis of Timing Parameters Beyond Decidability.Proc. 33rd Intl. Conf. ComputerAided Verification (CAV 2021)2021, 552565
 66 articleRewriteBased Equational Theorem Proving with Selection and Simplification.Journal of Logic and Computation431994, 217247
 67 bookRefinement calculusA systematic introduction.Springer Verlag1998
 68 incollectionSatisfiability Modulo Theories.Handbook of Satisfiability185Frontiers in Artificial Intelligence and ApplicationsIOS PressFebruary 2009, 26825885
 69 phdthesisSuperposition for HigherOrder Logic.Vrije Universiteit Amsterdam2021
 70 phdthesisStrong Connectivity and Shortest Paths for Checking Models.University of TwenteEnschede, The Netherlands2019
 71 inproceedingsA Datalog Hammer for Supervisor Verification Conditions Modulo Simple Linear Arithmetic.13th Intl. Symp. Frontiers of Combining Systems (FroCoS 2021)12941Lecture Notes in Computer ScienceSpringer2021, 324
 72 inproceedingsDeciding the BernaysSchoenfinkel Fragment over Bounded Difference Constraints by Simple Clause Learning over Theories.22nd Intl. Conf. Verification, Model Checking, and Abstract Interpretation (VMCAI 2021)12597Lecture Notes in Computer ScienceSpringer2021, 511533
 73 miscSCL with Theory Constraints.October 2020
 74 inproceedingsTowards Dynamic Dependable Systems through EvidenceBased Continuous Certification.9th International Symposium On Leveraging Applications of Formal Methods, Verification and Validation (ISOLA 2021)2021
 75 bookFoundations of Chemical Reaction Network Theory.202Applied Mathematical SciencesSpringer2019
 76 inproceedingsReconstructing veriT Proofs in Isabelle/HOL.PxTP 2019  Sixth Workshop on Proof eXchange for Theorem Proving301https://arxiv.org/abs/1908.09480Natal, BrazilAugust 2019, 3650
 77 inproceedingsGeneralized Completeness for SOS Resolution and its Application to a New Notion of Relevance.28th Intl. Conf. Automated Deduction (CADE 28)12699Lecture Notes in Computer ScienceSpringer2021, 327343
 78 articleThe Systems Biology Markup Language (SBML): A Medium for Representation and Exchange of Biochemical Network Models.Bioinformatics1942003, 524531
 79 inproceedingsSignatureBased Abduction for Expressive Description Logics.KR2020, 592602
 80 articleAlgorithmic Reduction of Biological Networks with Multiple Time Scales.Mathematics in Computer Science153September 2021, 499  534
 81 bookSpecifying Systems.Boston, Mass.AddisonWesley2002
 82 articleBioModels Database: A Free, Centralized Database of Curated, Published, Quantitative Kinetic Models of Biochemical and Cellular Systems.Nucleic acids res.34suppl_1January 2006, D689D691
 83 articleTransmission Dynamics and Control Strategies Assessment of Avian Influenza A (H5N6) in the Philippines.Infectious Disease Modelling32018, 3559
 84 bookProgramming from Specifications.2nd editionPrentice Hall1998
 85 articleA Variant of the Superposition Calculus.Arch. Formal Proofs20162016
 86 inproceedingsFaster, Higher, Stronger: E 2.3.CADE11716LNCSSpringer2019, 495507
 87 inproceedingsAlethe: Towards a Generic SMT Proof Format (extended abstract).Seventh Workshop on Proof eXchange for Theorem Proving (PxTP 2021)336EPTCS2021, 4954
 88 inproceedingsReliable Reconstruction of FineGrained Proofs in a Proof Assistant.28th Intl. Conf. Automated Deduction (CADE 28)2021