Keywords
Computer Science and Digital Science
 A2.1.7. Distributed programming
 A2.1.11. Proof languages
 A2.4. Formal method for verification, reliability, certification
 A2.4.1. Analysis
 A2.4.2. Modelchecking
 A2.4.3. Proofs
 A2.5. Software engineering
 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]
 Thomas Sturm [CNRS, Senior Researcher, HDR]
 Uwe Waldmann [Max Planck Society]
 Christoph Weidenbach [Max Planck Society, HDR]
Faculty Members
 Étienne André [Univ de Lorraine, Professor, HDR]
 Marie DuflotKremer [Univ de Lorraine, Associate Professor]
 Dominique Méry [Univ de Lorraine, Professor, HDR]
 Sorin Stratulat [Univ de Lorraine, Associate Professor]
PostDoctoral Fellows
 Martin Bromberger [Max Planck Society]
 Zheng Cheng [Univ de Lorraine]
 Yann Duplouy [Inria, until Oct 2020]
 Mathieu Montin [Univ de Lorraine, from Nov 2020]
 Hamid Rahkooy [CNRS, until Jul 2020, Max Planck Society from Aug 2020]
 Sophie Tourret [Max Planck Society]
 Marco Voigt [Max Planck Society, until Feb 2020]
PhD Students
 Antoine Defourné [Inria]
 Margaux Duroeulx [Univ de Lorraine, until Apr 2020]
 Daniel El Ouraoui [Inria]
 Mathias Fleury [Max Planck Society, until Jan 2020]
 Alexis Grall [Univ de Lorraine, until Sep 2020]
 Fajar Haifani [Max Planck Society]
 Pierre Lermusiaux [Univ de Lorraine]
 Hans Jorg Schurr [Inria]
Interns and Apprentices
 Heba Al Kayed [Inria, from Mar 2020 until Jul 2020]
 Adele Barbier [Univ de Lorraine, from Apr 2020 until Jun 2020]
 Amelie Ferstler [Univ de Lorraine, from May 2020 until Jun 2020]
 Aleksander Kryukov [Univ de Lorraine, from Mar 2020 until Jul 2020]
 Raphael Le Bihan [Inria, from Jun 2020 until Jul 2020]
 Mathieu Tabary [Univ de Lorraine, from Apr 2020 until Jun 2020]
 Cristian Vargas Montero [Univ de Lorraine, from Mar 2020 until Jul 2020]
Administrative Assistants
 Sophie Drouot [Inria]
 Sylvie Hilbert [CNRS]
Visiting Scientist
 Masaki Waga [Univ de Lorraine, Jan 2020]
External Collaborators
 Jasmin Christian Blanchette [Université libre d'Amsterdam  PaysBas]
 Pascal Fontaine [Université de Liège, HDR]
 Igor Konnov [Informal Systems, on leave from Inria]
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 proved 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 in 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 superposition 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.
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 proof platforms developed by other groups, and participate in international competitions. We also validate our work on proof 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 verification, we pursue applications of some of the symbolic techniques that we are developing 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 SEIR 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 62 and a theory solver for linear arithmetic 2.
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 1 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 TLA+71 specifications. 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.
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 refinement60, 63, 76 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.
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. Yesterday, simple models of 2 to 5 ordinary differential equations were used to illustrate fundamental ideas such as multistationarity or biological rhythms sustained by biological cells. Even such simple models required involved analysis, justifying 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 74 currently contains thousands of handbuilt models of up to several hundreds of variables. Much quicker analysis is also needed. In precision medicine one wants to be able to move from hypotheses to their verification in minutes. Numerical analysis of large models often fails to meet these desiderata because it either requires an exhaustive scan of the parameter space or the identification of the numerical parameters from data. Both tasks are impossible 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. An alternative to numerical methods is the use of symbolic methods, which can be used to compute bifurcation and phase diagrams of biological models, which are very useful tools for decision.
It turns out that, from a computational point of view, many problems in that field combine algebraic questions with combinatorics, for which we have found that SMT solving over various theories is an excellent tool. When generalizing to parametric variants of the considered problems, firstorder quantifier elimination methods over complex numbers, real numbers, or integers enter the stage.
Members of VeriDis have carried out considerable research on applications of symbolic techniques in systems biology, especially since the launch of the interdisciplinary SYMBIONT project in 2018 (section 9.3).
4 Application domains
Distributed algorithms and protocols are found at all levels of computing infrastructure, from manycore processors and systemsonchip 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.
We have also targeted applications with respect to cybersecurity, notably within the ANRNRF ProMiS project. In 23, we proposed a new definition of noninterference for parametric timed automata, an extension of finitestate automata with clocks and timing parameters (unknown constants) 61. We proposed a method to quantify the minimal frequency of attack actions for their attack to succeed (or, put differently, the maximal frequency of internal actions so that there is no leak to an external observer). We inferred values of the minimal time between two consecutive actions of the attacker, so that (s)he disturbs the discrete behavior (set of reachable locations). We also synthesized valuations for the timing constants of the automaton (seen as parameters) guaranteeing noninterference.
5 Highlights of the year
5.1 Awards
 The paper33, prepared in cooperation with colleagues from the University of Iowa and Stanford University, received a best paper award at IJCAR 2020. We proved that theories of algebraic data types such as lists or trees, as present in the SMTLIB language, exhibit interesting properties that enable to integrate them nicely in a combination of decision procedures in SMT reasoning.
 The prover Zipperposition, developed by Blanchette, Tourret, Waldmann, and their colleagues in the context of the Matryoshka project (cf. section 9.2.1), finished in first place in the higherorder proving division of the 2020 edition of the CADE ATP System Competition2, over 20 percentage points ahead of the nearest competitor. This breakthrough was possible thanks to the theoretical work done by team members, notably the design of the superposition calculus with lambdaabstractions mentioned in last year's report. Zipperposition was initially developed by Simon Cruanes, who was a senior engineer in the VeriDis team from 2015 to 2017.
 Martin Bromberger won the EAPLS dissertation award3. Citing the summary of
the jury's findings
 The problems addressed in this thesis are highly relevant and extremely challenging.
 The excellent results obtained in this thesis advance the state of the art of SMT solving and theorem proving in an outstanding way.
 The thesis presents breakthroughlike achievements in a wellestablished and researched field with an immediate impact and advancement of the field.
 The presented procedures offer significant improvements over the state of the art that has been adopted in professional SMT provers.
6 New software and platforms
6.1 New software
6.1.1 Redlog
 Name: Reduce Logic System
 Keywords: Computer algebra system (CAS), Firstorder logic, Constraint solving

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, and many more.

News of the Year:
Parts of the Redlog code are 25 years old now. Version 1 of the underlying computer algebra system Reduce has been published even 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.
During 2020 we implemented and launched an integrated documentation and online help system, which is available interactively in the software itself as well as online on the Redlog website via an interactive GUI. The website also features a RESTful interface to the documentation. In that course, the website has undergone a total redesign, now using stateoftheart web technologies and frameworks such as Angular and Bootstrap.

URL:
https://
www. redlog. eu/  Contact: Thomas Sturm
 Participant: Thomas Sturm
6.1.2 SPASSSATT
 Name: SPASSSATT
 Keywords: Automated deduction, Decision

Functional Description:
SPASS SATT is an SMT solver for the theories of linear integer arithmetic, linear rational arithmetic and mixed linear arithmetic. It features new tests for the satisfiability of unbounded systems, as well as new algorithms for the detection of integer solutions.
We further investigated the use of redundancy elimination in SAT solving and underlying implementation techniques. Our aim is a new approach to SAT solving that needs fewer conflicts (on average) and is faster than the current stateofthe art solvers. Furthermore, we have developed a new calculus and first prototypical implementation of a SAT solver with mixed OR/XOR clauses and are currently adapting our algorithms to support SUPERLOG reasoning.
 News of the Year: SPASSSATT participated in the SMT competitions 20182019 in the quantifier free integer and rational linear arithmetic categories and won one category each year, respectively. We have stopped entering the competition, but the competition designers run previous years winners. Our 2019 version scored second in the rational linear arithmetic category in 2020.

URL:
https://
www. mpiinf. mpg. de/ departments/ automationoflogic/ software/ spassworkbench/ spasssatt/  Contacts: Martin Bromberger, Christoph Weidenbach
 Participants: Martin Bromberger, Mathias Fleury, Christoph Weidenbach
6.1.3 veriT
 Keywords: Automated deduction, Formula solving, Verification
 Functional Description: VeriT is an open, trustable and efficient SMT (Satisfiability Modulo Theories) solver. It comprises a 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 2020 have been focused on quantifier handling, higher logic, and better proof production.
The veriT solver participated in the SMT competition
SMTCOMP 2020http://www.smtcomp.org with good results. In particular, our fast version (tuned for 24s) was among the fastest (besides portfolio approaches) for several logics, in the 24s category. We target applications where validation of formulas is crucial, such as the validation of TLA+ and B specifications, and 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:
http://
www. veriTsolver. org  Authors: David Déharbe, Pascal Fontaine, Diego Caminha B. De Oliveira, Haniel Barbosa, Thomas Bouton, Daniel El Ouraoui, HansJörg Schurr
 Contact: Pascal Fontaine
 Participants: Haniel Barbosa, Daniel El Ouraoui, Pascal Fontaine, HansJörg Schurr
 Partner: Université de Lorraine
6.1.4 TLAPS
 Name: TLA+ proof system
 Keyword: Proof assistant
 Functional Description: TLAPS is a platform for developing and mechanically verifying proofs about TLA+ specifications. 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.
 News of the Year: In 2020, we published a minor release, fixing some issues notably for the SMT backend. Substantial work was devoted to supporting liveness reasoning, in particular proofs about the enabled and action composition constructions of TLA+. We also prepared support for current versions of the Isabelle backend prover.

URL:
https://
tla. msrinria. inria. fr/ tlaps/ content/ Home. html  Contacts: Stephan Merz, Damien Doligez
 Participants: Damien Doligez, Stephan Merz, Ioannis Filippidis
 Partner: Microsoft
6.1.5 Apalache
 Name: Abstractionbased Parameterized TLA+ Checker
 Keyword: Model Checker

Scientific Description:
Apalache is a symbolic model checker that works under the following assumptions:
(1) As in TLC, all specification parameters are fixed and finite, e.g., the system is initialized integers, finite sets, and functions of finite domains and codomains. (2) As in TLC, all data structures evaluated during an execution are finite, e.g., a system specification cannot operate on the set of all integers. (3) Only finite executions up to a given bound are analysed.
In 2019, we have simplified the set of rewriting rules, which are used in the translation from TLA+ to SMT. We have shown that the rules are sound, that is, that the translator produces a set of SMT constraints that are equisatisfiable to the given TLA+ formula. We have conducted the experiments on 10 TLA+ specifications of distributed algorithms. When running bounded model checking, Apalache outperforms TLC in some cases. When checking inductive invariants, Apalache runs significantly faster than TLC. These results were reported at ACM OOPSLA 2019.
Apalache translates bounded executions of a TLA+ specifications into a set of quantifierfree SMT constraints. By querying the SMT solver, the model checker either finds a counterexample to an invariant, or proves that there is no counterexample up to given computation length.
 Functional Description: Version 0.5.0 implements a symbolic bounded model checker for TLA+ that runs under the same assumptions as the explicitstate model checker TLC. It checks whether a TLA+ specification satisfies an invariant candidate by checking satisfiability of an SMT formula that encodes: (1) an execution of bounded length, and (2) preservation of the invariant candidate in every state of the execution. Our tool is still in the experimental phase, due to a number of challenges posed by the semantics of TLA+ to SMT solvers.

Release Contributions:
Version 0.10.0 introduces multiple features in comparison to version 0.5.0:
 the new type checker Snowcat that works independently of the model checker's pipeline  the new assignment finder that delivers an improved user experience  an improved build system and continuous integration development  support for TLC configuration files  an improved SMT encoding for set cardinalities  support for recursive operators and recursive functions  support for advanced language features such as local instances, local operators, lambdas, etc.  support for offline and online SMT solvers

News of the Year:
In 2020, the tool was mainly developed at TU Wien and Informal Systems. The verification team of Informal Systems applied Apalache for model checking of several blockchain protocols in TLA+. Importantly, Apalache was the only tool that could cope with those specifications, as these protocols operate under Byzantine faults and time constraints.
We have improved the overall tool stability and accounted for the feedback that was provided to us by the tool users at Informal Systems. Notably, we have found that the type checker and assignment finder were the main bottlenecks from the users' point of view. To this end, we have implemented a new type checker that expects type annotations in a simple format. The new type checker is able to find types of many operators by constraint solving.
Moreover, we have also developed a completely automatic type inference tool. However, this tool is still in the prototype phase, and it needs a good amount of work to become a mature tool.

URL:
https://
github. com/ informalsystems/ apalache  Publications: hal01899719v1, hal01871131v1, hal02280888v1
 Contact: Igor Konnov
 Partners: Technische Universität Wien, Informal Systems
6.1.6 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: New algorithm for NDFSbased cycle synthesis (by Laure Petrucci and Jaco Van de Pol). Extension of the syntax: ifthenelse conditions allowed in updated, #include allowed for submodel inclusion. New applications to cybersecurity.

URL:
https://
www. imitator. fr/  Publications: hal00785289, hal02153214, hal02153342, hal01961496
 Contact: Etienne Andre
 Participants: Etienne Andre, Jaime Eduardo Arias Almeida
 Partner: Loria
7 New results
7.1 Automated and Interactive Theorem Proving
Participants: Jasmin Christian Blanchette, Martin Bromberger, Antoine Defourné, Daniel El Ouraoui, Mathias Fleury, Pascal Fontaine, Fajar Haifani, Raphaël Le Bihan, Stephan Merz, HansJörg Schurr, Sorin Stratulat, Sophie Tourret, Marco Voigt, Uwe Waldmann, Christoph Weidenbach.
7.1.1 Contributions to SMT Techniques
Combination of Satisfiability Procedures.
A satisfiability problem is often expressed in a combination of theories, and a natural approach consists in solving the problem by combining the satisfiability procedures available for the component theories. This is the purpose of the combination method introduced by Nelson and Oppen. However, in its initial presentation, the NelsonOppen combination method requires the theories to be signaturedisjoint and stably infinite. The design of a generic combination method for nondisjoint unions of theories is difficult, but it is worth exploring simple nondisjoint combinations that appear frequently in verification. An example is the case of shared sets, where sets are represented by unary predicates. Another example is the case of bridging functions between data structures and a target theory (e.g., a fragment of arithmetic).
In 2015, we defined a sound and complete combination procedure à la NelsonOppen for the theory of absolutely free data structures (including lists and trees) connected to another theory via bridging functions 67. This combination procedure has also been refined for standard interpretations. The resulting theory has a nice politeness property, enabling combinations with arbitrary decidable theories of elements. We also investigated other theories 68 amenable to similar combinations: this class includes the theory of equality, the theory of absolutely free data structures, and all the theories in between.
In 2018 and 2019, we have been improving the framework and unified both results. This was published in the Journal of Automated Reasoning in 2020 17.
The above works pave the way for combinations involving the theory of algebraic datatypes as found in the SMTLIB. Together with colleagues in Iowa and Stanford, this was published at IJCAR 2020 33. This article received a best paper award.
Quantifier Handling in SMT.
SMT solvers generally rely on various instantiation techniques for handling quantifiers. We built a unifying framework encompassing quantified formulas with equality and uninterpreted functions, such that the major instantiation techniques in SMT solving can be cast in that framework. It is based on the problem of Eground (dis)unification, a variation of the classic Rigid Eunification problem. We introduced a sound and complete calculus to solve this problem in practice: Congruence Closure with Free Variables (CCFV). Experimental evaluations of implementations of CCFV demonstrate notable improvements in the stateoftheart solver CVC4 and make the solver veriT competitive with stateoftheart solvers for several benchmark libraries, in particular those originating in verification problems.
In 2019 and 2020, we investigated machine learning techniques for predicting the usefulness of an instance in order to decrease the number of instances passed to the SMT solver. For this, we proposed a meaningful way to characterize the state of an SMT solver, to collect instantiation learning data, and to integrate a predictor in the core of a stateoftheart SMT solver. This ultimately leads to more efficient SMT solving for quantified problems.
HigherOrder SMT.
SMT solvers have throughout the years been able to cope with increasingly expressive formulas, from ground logics to full firstorder logic (FOL). In contrast, the extension of SMT solvers to higherorder logic (HOL) was mostly unexplored. We proposed a pragmatic extension for SMT solvers to support HOL reasoning natively without compromising performance on FOL reasoning, thus leveraging the extensive research and implementation efforts dedicated to efficient SMT solving. We showed how to generalize data structures and the ground decision procedure to support partial applications and extensionality, as well as how to reconcile quantifier instantiation techniques with higherorder variables. We also discussed a separate approach for redesigning an SMT solver for higherorder logic from the ground up via new data structures and algorithms. We applied our pragmatic extension to the CVC4 SMT solver and discussed a redesign of the veriT SMT solver. Our evaluation showed that they are competitive with stateoftheart HOL provers and often outperform the traditional encoding into FOL.
This result was published at CADE 2019 64. Work in 2020 focused on extending the CCFV algorithm to higherorder logic 41: the firstorder algorithm is not directly usable since it strongly relies on the fact that functions are fully applied, and no variable can appear in a function place. It is also necessary to find a radically different approach. Our approach is to work on an encoding of the CCFV higherorder problem into SAT.
Proofs for SMT.
We have 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. In 2019, the format of proof output was further improved, while also improving the reconstruction procedure in the proof assistant Isabelle/HOL. This allowed the tactic using SMT with proofs to be regularly suggested by Sledgehammer as the fastest method to automatically solve proof goals. This was the subject of a workshop publication in 2019 69. In 2020, we have made steady progress on this front, and thanks to this progress, the veriT solver has been integrated into Isabelle with full support of reconstruction for veriT proof. This lead to improvements in the Sledgehammer facility to automatically discharge Isabelle proofs.
Theory Solving for QuantifierFree Linear Integer Arithmetic.
In 16 we consolidate our research in effective methods for the existential theory of Presburger Arithmetic over the past years in a journal article. We consider feasibility of linear integer problems in the context of verification systems such as SMT solvers or theorem provers. Although satisfiability of linear integer problems is decidable, many stateoftheart implementations neglect termination in favor of efficiency. We present the calculus CutSat++ that is sound, terminating, complete, and leaves enough space for model assumptions and simplification rules in order to be efficient in practice. CutSat++ combines modeldriven reasoning and quantifier elimination to the feasibility of linear integer problems.
7.1.2 Certification of automated reasoning techniques
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, such as CDCL (Conflict Driven Clause Learning), ordered resolution, or superposition.
For CDCL we have been able to derive the stateoftheart algorithms from a simple, verified core, inheriting its properties via instantiation. Then we could further refine this setting up to the generation of executable code that performs surprisingly well compared to handcoded CDCL implementations 50.
The framework relies on modular extensions of lifted redundancy criteria that underlie the deletion of subsumed formulas. In presentations of proof calculi, this aspect is usually only discussed informally. Our framework allows us to extend redundancy criteria so that they cover subsumption, and also to model entire prover architectures in such a way that the static refutational completeness of a calculus immediately implies the dynamic refutational completeness of a prover implementing the calculus, for instance within an Otter or DISCOUNT loop. Our framework is mechanized in Isabelle/HOL. This research was presented at IJCAR 2020 35.
Certifying Cyclic Induction Reasoning for Firstorder Logic with Admissible Predicates.
The Coq proof assistant is powerful enough to reproduce cyclic reasoning for firstorder logic with inductive definitions (FOL${}_{\text{ID}}$) in terms of cyclic proofs. We identify a class of Coqcertifiable cyclic proofs convertible to a set of Coq proofs relying on normalized wellfounded explicit induction. These proofs start with a unique explicit induction step whose induction schema is derived from the definition of new admissible predicates. The admissibility property, as well as the rest of the proofs, can be deduced from the input proof. The conversion procedure does not backtrack and no extra reconstruction proof techniques are needed. In practice, it has been used to certify FOL${}_{\text{ID}}$Cyclist proofs, including a proof for the 2Hydra problem, and nontrivial cyclic SPIKE proofs of conjectures about conditional specifications.
7.1.3 Automated reasoning for specific logics
Signaturebased abduction.
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.
Signaturebased abduction aims at building hypotheses over a specified set of names, the signature, that explain an observation relative to some background knowledge. This type of abduction is useful for tasks such as diagnosis, where the vocabulary used for observed symptoms differs from the vocabulary expected to explain those symptoms. In the description logic literature, abduction has received little attention, despite being recognised as important for ontology repair, query update and matchmaking.
S. Tourret, together with P. Koopmann, W. DelPinto and R. Schmidt, presented the first complete method solving signaturebased abduction for observations expressed in the expressive description logic $\mathrm{\mathcal{A}\mathcal{L}\mathcal{C}}$30. The method is guaranteed to compute a finite and complete set of hypotheses, and is evaluated on a set of realistic knowledge bases.
In joint work with P. Koopmann, we are currently investigating an alternative approach to abduction for description logics based on a translation to firstorder logic and back. This work is motivated by the recent development of efficient tools for abductive reasoning in firstorder logic.
Relevance of clauses for resolution.
In joint work with P. Koopmann 39, we define a notion of relevance of a clause for proving a particular entailment by the resolution calculus. We think that our notion of relevance is useful for explaining why an entailment holds. A clause is relevant if there is no proof of the entailment without it. It is semirelevant if there is a proof of the entailment using it. It is irrelevant if it is not needed in any proof. By using wellknown translations of description logics to firstorder clause logic, we show that all three notions of relevance are decidable for a number of description logics, including $\mathrm{\mathcal{E}\mathcal{L}}$ and $\mathrm{\mathcal{A}\mathcal{L}\mathcal{C}}$. We provide effective tests for (semi)relevance. The (semi)relevance of a DL axiom is defined with respect to the (semi)relevance of the respective clauses resulting from the translation.
This notion of semirelevance is particularly interesting and can be detected using SOSresolution derivations. We are currently working on a generalized proof of the SOS strategy for resolution to validate the theory behind the tests for semirelevance in firstorder logic.
Derivation reduction for SLD resolution.
Inductive Logic Programming (ILP) is a form of machine learning that induces hypotheses from examples and background knowledge. Many forms of ILP use secondorder Horn clauses as templates, also denoted as metarules, to learn logic programs, and several of them rely on SLD resolution to produce new candidate solutions. Determining which metarules to use for a given learning task is a major open problem in ILP and most approaches use clauses provided by the designers of the systems without any theoretical justifications.
In joint work with A. Cropper we formalized the derivation reduction problem for SLD resolution, the undecidable problem of finding a finite subset of a set of clauses from which the whole set can be derived using SLD resolution. We studied the reducibility of various fragments of secondorder Horn logic that are relevant in ILP and extended our results to standard resolution. We also conducted an empirical study of the effects of using reduced sets of such metarules on the overall learning accuracy and time, which shows a substantial improvement over the state of the art, in addition to the theoretical guarantees offered.
Towards Improved Encodings of TLA+ Proof Obligations.
We reconsider the encoding of proof obligations that arise in proofs about TLA+ specifications in multisorted firstorder logic. In his PhD thesis, Antoine Defourné studies correctness criteria for assigning types to TLA+ expressions, based on embeddings between models for different logics. The objective is to delineate what type assignments are sound when translating from the untyped TLA+ language into the multisorted logics underlying typical automated reasoning engines.
He also implemented a new backend reasoner based on Zipperposition for handling proof obligations that involve features of higherorder logic such as function or predicate variables that may appear in TLA+ proof sequents. The design of this backend was presented at JFLA 2020 38, and a working prototype at the TLA+ Community Meeting 37.
During his undergraduate internship, Raphaël Le Bihan revisited the coalescing technique used in TLAPS for separating firstorder and modal reasoning.
7.2 Formal Methods for Developing and Analyzing Algorithms and Systems
Participants: Heba Al Kayed, Étienne André, Martin Bromberger, Zheng Cheng, Marie DuflotKremer, Yann Duplouy, Margaux Duroeulx, Alexis Grall, Igor Konnov, Aleksander Kryukov, Dominique Méry, Stephan Merz, Mathieu Montin, Christoph Weidenbach.
7.2.1 Contributions to Formal Methods of System Design
Simpler Rules for Auxiliary Variables.
Refinement of a specification expressed at a high level of abstraction by a lowerlevel specification is a fundamental concept in formal system development. A key problem in proving refinement is to demonstrate that suitable values of internal variables of the highlevel specification can be assigned to every possible execution of the lowlevel specification. The standard technique for doing so is to exhibit a refinement mapping where values for these variables are computed for each state, but it is also well known that this technique is not complete. In joint work with Leslie Lamport (Microsoft Research), we revisit the classic paper 59 that introduced constructions for auxiliary variables in order to strengthen the refinement mapping technique. In particular, we introduce simpler rules for defining prophecy variables and demonstrate how they can be used for proving the correctness of an algorithm implementing a linearizable object. We also show that our constructions of auxiliary variables yield a complete proof method. An article based on this work has been submitted for publication to a journal.
Generating Distributed Programs from EventB Models.
In 25 we present an approach for combining correctbyconstruction approaches and transformations of formal models expressed in EventB to executable programs written in DistAlgo, a domainspecific language embedded in Python. Our objective is to address the design of verified distributed programs. We define a subset LB (Local EventB) of the EventB modelling language restricted to events modelling typical actions of distributed programs, including internal or local computations, as well as sending and receiving messages. We define transformations of the various elements of the LB language into DistAlgo programs. The general methodology consists in starting from a statement of the algorithmic problem and then progressively producing an LB model obtained after several refinement steps of the initial LB model. The derivation of the LB model has already been addressed in previous research. The transformation of LB models into DistAlgo programs is illustrated through a simple example. The refinement process and the soundness of the transformation allow one to produce correctbyconstruction distributed programs.
An Extension of PlusCal for Distributed Algorithms.
PlusCal 72 is a language for describing algorithms. It has the look and feel of pseudocode, but also has a formal semantics through a translation to TLA+ specifications. During her master internship, Heba Al Kayed extended the PlusCal language and translator so that it is more suitable for modeling distributed algorithms. As a first extension, parallel processes may have several code blocks that represent threads communicating through local variables. Second, communication channels are introduced as firstclass entities, together with send, multicast, and receive operations. This work was presented at the TLA+ Community Meeting 36.
Formal Analysis of Critical Interactive Systems.
When interactive systems allow users to interact with critical systems, they are qualified as Critical Interactive Systems. Their design requires the support of different activities and tasks to achieve user goals. Examples of such systems are cockpits, nuclear plant control panels, medical devices, etc. Such critical systems are very difficult to model due to the complexity of the offered interaction capabilities. In joint work with Ismaël Mendil, Neeraj Kumar Singh, Yamine AïtAmeur, and Philippe Palanque (IRIT Toulouse), we present 31 a formal framework, F3FLUID (Formal Framework For FLUID), for designing safetycritical interactive systems. It relies on FLUID as the core modelling language. FLUID enables modelling and using interactive systems domain concepts and supports an incremental design of such systems. Formal verification, validation and animation of the designed models are supported through different transformations of FLUID models into target formal verification techniques: EventB for formal verification, ProB model checker for animation and Interactive Cooperative Objects for user validation. The EventB models are generated from FLUID while ICO and ProB models are produced from EventB. We exemplify the reallife case study TCAS (Traffic alert and Collision Avoidance System) to demonstrate our framework.
7.2.2 Automated Reasoning Techniques for Verification
Towards Mechanization and Application of SUPERLOG.
In joint work with Markus Kroetzsch and Christof Fetzer (Technical University of Dresden), we have introduced a logical fragment called SUPERLOG (Supervisor Logic) that is meant to provide a basis for formalizing abstract control algorithms found in ECUs (Electronical Control Unit), plus fully automated verification, plus execution 28. Technically, the language is an extension of the firstorder BernaysSchoenfinkel fragment with arithmetic constraints. It extends the well known SMT fragment by universally quantified variables. We have developed a sound and complete calculus for the SUPERLOG language 51. The calculus supports nonexhaustive propagation and can therefore be a role model for other calculi where exhaustive propagation cannot be afforded 16. Based on the decidability results obtained by Marco Voigt 77, we are working on fully automatic verification approaches for fragments of the SUPERLOG language. One line of research is to “hammer” verification conditions in SUPERLOG fragments to DATALOG 66 for efficient solving. The other is to use abstractions guiding the search of the calculus, related to our abstraction refinement approach 22.
Satisfiability Techniques for Reliability Assessment.
Margaux Durœulx defended her PhD thesis 49, funded by the excellence program of University of Lorraine and prepared in cooperation with Nicolae Brînzei (Centre de Recherche en Automatique de Nancy). The thesis studies the use of satisfiability techniques for assessing the reliability of complex systems, represented by static or dynamic fault trees that determine which combinations of component failures lead to system failures. Based on encodings of fault trees in propositional logic, a SAT solver can be used to compute minimal tie sets or sequences, and these are instrumental for probabilistic realiability assessment.
7.2.3 Verification of Quantitative Systems or Properties
Statistical Model Checking of Distributed Programs.
We completed in 2020 our work on developing a prototype tool for performing statistical model checking within the SimGrid framework. The goal was to give users the opportunity, in one single framework, to take advantage of both verification and simulation possibilities. To do so, we added to SimGrid the possibility to use stochastic profiles, introducing probabilities in the model of the network. The prototype tool can be interfaced with the SimGrid simulator to perform statistical model checking on the actual programs simulated using the SimGrid framework. The prototype was evaluated on examples such as the Bit Torrent protocol in which we added a probabilistic model of node failures. This work resulted in a publication at the SIMULTECH conference 27.
Hybrid System Design with Safety Constraints.
Hybrid systems are characterized by the interaction of continuous dynamics and discrete control. As hybrid systems become ubiquitous and more and more complex, analysis and synthesis techniques for designing safe hybrid systems are in high demand. 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 operators and how to integrate traditional refinement in hybrid system design. In the same spirit, we 52 extend previous work by proposing a strategy that can coherently refine an abstract hybrid system design with safety constraints down to the concrete one with implementable discrete control that can behave safely. Our proposal is validated on the design of a smart heating system.
7.3 Verification and Analysis of Dynamic Properties of Biological Systems
Participants: Cristian Vargas Montero, Hamid Rahkooy, Thomas Sturm.
Geometric Analysis of Steady State Regimes.
Our work in toricity of steady state ideals of biomodels 70 from 2019 has been accepted for journal publication and will appear during 2021. The approach there was to automatically recognize relevant geometric structure of steady state varieties in ${K}^{n}$, where $K$ stands for either the complex or the real numbers. For the complex numbers we used quite complicated algebraic techniques based on Gröbner basis theory. For the real numbers, in contrast, our approach was purely based on logic. Technically we employed real quantifier elimination; SMTsolving in QF_NRA is a possible alternative, which has not been studied systematically. This year we managed to treat also the case of complex numbers on a purely logical basis 43, 56. Based on arguments from algebraic model theory, this also gives insights into the interdependencies of the occurrences of relevant geometric structures over the complex numbers versus the real numbers.
Geometric toricity of a variety resembles the algebraic concept of binomiality of the corresponding polynomial ideal. Generalizing that wellstudied binomiality concept of chemical reaction networks, in 42, 55 unconditional binomiality has been defined, its properties have been investigated and a linear algebra approach has been given for testing unconditional binomiality in the case of reversible reactions. A graph theoretical version of the linear algebra approach has been presented in 40.
Parametric Analysis of Steady State Regimes.
Joint work with Russell Bradford (Bath, UK), James Harold Davenport (Bath, UK), Matthew England (Coventry, UK), Hassan Errami (Bonn, Germany), Vladimir Gerdt (Dubna, Russia), Dima Grigoriev (Lille), Charles Hoyt (Bonn, Germany), Marek Košta (Bratislava, Slovak Republic), Ovidiu Radulescu (Montpellier), and Andreas Weber (Bonn, Germany)
In 15 we address, on the one hand, the simpler question whether or not there is are unique steady states, without going into details on the exact geometry. On the other hand, we do so in dependence on parametric reaction rates, so that the results are necessary and sufficient formal logical conditions in the Tarski Algebra. Again, the underlying methods are of logical nature, mostly real elimination methods like virtual substitution, cylindrical algebraic decomposition, and real triangular sets.Reduction of Reaction Network Kinetics to Multiple Timescales.
Joint work with Niclas Kruff (Aachen, Germany), Christoph Lüders (Bonn, Germany), Ovidiu Radulescu (Montpellier), Sebastian Walcher (Aachen, Germany)
Our interdisciplinary work 54 in computer science, mathematics, and systems biology is concerned with the reduction of a system of ordinary differential equations (in time) into several simpler subsystems, each corresponding to a certain orders of magnitude of velocities, also called time scales, of the corresponding differential variables. To our knowledge this is the first mathematically rigorous approach for reaction networks that allows for multiple time scales. Previous work either did not give any formal guarantees on the obtained results, or was limited to only two different time scales. 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.As an example consider a model related to the transmission dynamics of subtype H5N6 of the avian Influenza A virus in the Philippines in August 2017 75. That model is identified as BIOMD0000000716 in the BioModels database, a repository of mathematical models of biological processes 74. The model specifies four species: S_b (susceptible bird), I_b (infected bird), S_h (susceptible human), and I_h (infected human), the concentrations of which over time we denote by differential variables ${y}_{1},\cdots ,{y}_{4}$, respectively. The input system $S$ is given by
Our approach reduces this to three systems ${T}_{1}$, ${T}_{2}$, ${T}_{3}$ along with corresponding attractive manifolds ${\mathcal{M}}_{1}$, ${\mathcal{M}}_{2}$, ${\mathcal{M}}_{3}$:
Notice the explicit constant factors on the right hand sides of the differential equations. We see that the system ${T}_{2}$ is 125 times slower than ${T}_{1}$, and ${T}_{3}$ is another 125 times slower. The total computation time was about one second. Figure 1 visualizes the direction fields of ${T}_{1}$, ..., ${T}_{3}$ on ${\mathcal{M}}_{1}$, ..., ${\mathcal{M}}_{3}$, respectively.
This multiple time scale reduction of the bird flu model emphasizes a cascade of successive relaxations of different model variables. First, the population of susceptible birds relaxes, meaning that these variables reach quasisteady state values. This relaxation is illustrated in Fig. 1(b). Then the population of infected birds relaxes as shown in Fig. 1(c). Finally, the populations of susceptible and infected humans relax to a stable steady state as shown in Fig. 1(d), following a reduced dynamics described by ${T}_{3}$.
Real Singularities of Implicit Ordinary Differential Equations.
Joint Work with with Werner Seiler and Matthias Seiß (Kassel, Germany)
Implicit differential equations, i.e. equations which are not solved for a derivative of highest order, appear in many applications. In particular, the socalled differential algebraic equations may be considered as a special case of implicit equations. Compared with equations in solved form, implicit equations are more complicated to analyze and show a much wider range of phenomena. Already basic questions about the existence and uniqueness of solutions of an initial value problem become much more involved. One reason is the possible appearance of singularities.In 57 we discuss the effective computation of geometric singularities of implicit ordinary differential equations over the real numbers using methods from logic. Via the Vessiot theory of differential equations, geometric singularities can be characterized as points where the behaviour of a certain linear system of equations changes. These points can be discovered using a specifically adapted parametric generalisation of Gaussian elimination combined with real quantifier elimination methods and other logicbased simplification techniques. We demonstrate the relevance and applicability of our approach with computational experiments using a prototypical implementation based on Reduce and Redlog.
A key novelty of our approach is to consider the decisive linear system determining the Vessiot spaces first, independently of the given differential system. This allows us to make maximal use of the linearity and to apply a wide range of heuristic optimizations. Compared with the more comprehensive approach of 73, this also leads to an increased flexibility and we believe that the new approach will be in general more efficient in the sense that fewer cases will be returned.
8 Bilateral contracts and grants with industry
8.1 Bilateral Contracts with Industry
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.
9 Partnerships and cooperations
9.1 International Research Visitors
9.1.1 Visits of International Scientists
Masaki Waga from NII Tokyo (now at Kyoto University) visited the team in January and worked with Étienne André.
9.1.2 Visits to International Teams
Thomas Sturm visited the research group of Werner Seiler at the University of Kassel, Germany, during February 20–21, 2020. The primary topic was joint research on logicbased methods in the area of singularities of implicit ordinary differential equations.
International travel was essentially impossible from March 2020 due to the Covid pandemic.
9.2 European Initiatives
9.2.1 FP7 & H2020 Projects
Matryoshka
 Program: ERC
 Title: Fast Interactive Verification through Strong HigherOrder Automation
 Duration: April 2017 – March 2022
 Coordinator: Jasmin Blanchette (VU Amsterdam)
 Partners: Université de Lorraine (France)
 Inria contact: Stephan Merz
 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 (HO) 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:
https://
matryoshkaproject. .github. io
9.2.2 Collaborations in European Programs, except FP7 and H2020
PIAF
 Program: Erasmus+
 Title: Pensée Informatique et Algorithmique au Fondamental / Computational and Algorithmic Thinking in Primary Education
 Duration: September 2018 – August 2021
 Coordinator: Université de Liège
 Partners: Université du Luxembourg, Saarland University, ESPE Nancy
 Inria contact: Marie DuflotKremer
 Summary: The goal of the PIAF project is threefold: creating a repository of skills related to computational and algorithmic thinking, designing activities aiming at the acquisition of these skills, and evaluating the impact of these activities on primary school children and their computational thinking capacities.
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, RWTH Aachen, Eszterhazy Karoly University, Université de Lorraine.
 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.
9.3 National Initiatives
ANR International Project ProMiS
 Title: Provable Mitigation of Side Channel through Parametric Verification
 Duration: November 2019 – April 2022.
 Coordinators: Étienne André and Jun Sun (Singapore Management University, Singapore).
 Partners: École Centrale Nantes, Singapore University of Technology and Design.
 Participant: Étienne André

Summary:
ProMiS is an international project, funded by ANR in France and by NRF in Singapore under the PRCI program.
The Spectre vulnerability has recently been reported, which affects most modern processors. The idea is that attackers can extract information about the private data using a timing attack. It is an example of side channel attacks, where secure information flows through side channels unintentionally. How to systematically mitigate such attacks is an important and yet challenging research problem.
We propose to automatically synthesize mitigation of side channel attacks (e.g., timing or cache) using welldeveloped verification techniques. The idea is to reduce this problem to the parameter synthesis problem of a given formalism (for instance, parametric timed automata). Given a program or system with design parameters which can be tuned to mitigate side channel attacks, our approach will automatically generate provably secure valuations of the parameters. We plan to deliver a toolkit which can be automatically applied to realworld systems.

More information:
https://
www. loria. science/ ProMiS/
ANR International Project SYMBIONT
 Title: Symbolic Methods for Biological Networks
 Duration: July 2018–April 2022
 Coordinators: Thomas Sturm and Andreas Weber/Reinhard Klein (Univ. of Bonn, Germany)
 Partners: Univ. of Lille 1, Univ. of Montpellier, Inria Saclay Île de France (Lifeware), RWTH Aachen (Department of Mathematics and Joint Research Center for Computational Biomedecine), Univ. of Kassel
 Participants: Thomas Sturm, Hamid Rahkooy
 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:
https://
www. symbiontproject. org/
ANR Project Formedicis
 Title: Formal methods for the development and the engineering of critical interactive systems
 Duration: January 2017 – December 2021
 Coordinator: David Chemouil (Onera)
 Partners: ENSEEIHT/IRIT Toulouse, ENAC, Université de Lorraine
 Participants: 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.
ANR Project DISCONT
 Title: Correct integration of discrete and continuous models
 Duration: March 2018 – February 2023
 Coordinator: Dominique Méry
 Partners: ENSEEIHT/IRIT Toulouse, LACL, ClearSy, Université de Lorraine
 Participants: Dominique Méry, Zheng Cheng
 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.

More information:
https://
discont. loria. fr/
ANR Project PARDI
 Title: Verification of parameterized distributed systems
 Duration: January 2017 – December 2021
 Coordinator: Philippe Quéinnec (ENSEEIHT/IRIT Toulouse)
 Partners: Université Paris Sud/LRI, Université Nanterre/LIP6, Inria Nancy – Grand Est
 Participants: Stephan Merz
 Summary: Distributed systems and algorithms are parameterized by the number of participating processes, the communication model, the fault model, and more generally the properties of interaction among the processes. The project aims at providing methodological and tool support for verifying parameterized systems, using combinations of model checking and theorem proving. VeriDis contributes its expertise on TLA+ and its verification tools, and the integration with the Cubicle model checker is a specific goal of the project.

More information:
http://
pardi. enseeiht. fr/
PIA2 ISITE LUE  Digitrust
 Title: Lorraine Université d'Excellence, Citizen Trust in the Digital World
 Duration: 2016 – 2020
 Coordinator: Marine Minier
 Participants: Margaux Durœulx, Stephan Merz
 Summary: Digitrust is one of the “impact” projects within the excellence funding acquired by University of Lorraine and supports research into different aspects related to the trustworthiness and security of digital systems. It funded the PhD thesis of Margaux Durœulx on the use of SAT techniques for assessing system reliability.
Inria IPL HAC SPECIS
 Title: Highperformance application and computers: studying performance and correctness in simulation
 Duration: June 2016 – June 2020
 Coordinator: Arnaud Legrand (CNRS & Inria Grenoble Rhône Alpes, Polaris)
 Partners: Inria Grenoble Rhône Alpes (Avalon), Inria Rennes Bretagne Atlantique (Myriads), Inria Bordeaux Sud Ouest (Hiepacs, Storm), Inria Saclay Île de France (Mexico), Inria Nancy Grand Est (Veridis)
 Participants: Marie DuflotKremer, Yann Duplouy, Stephan Merz
 Summary: The goal of HAC SPECIS was to allow the study of real HPC systems with respect to both correctness and performance. To this end, this Inria Project Lab assembled experts from the HPC, formal verification, and performance evaluation communities. VeriDis contributed its expertise in formal verification techniques. In particular, our goal was to extend the functionalities of exhaustive and statistical model checking within the SimGrid platform. The project was successfully evaluated in the fall of 2020.

More information:
http://
hacspecis. gforge. inria. fr
DFG Transregional Research Center 248 CPEC
 Title: Foundations of Perspicuous Software Systems.
 Duration: January 2019 – December 2022.
 Coordinators: Holger Hermanns (Saarland University, Germany) and Raimund Dachselt (University of Dresden, Germany).
 Partners: Saarland University, University of Dresden, Max Planck Institute for Software Systems, Saarbrücken.
 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 behaviour 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 behaviour. 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.

More information:
https://
www. perspicuouscomputing. science/
10 Dissemination
10.1 Promoting Scientific Activities
10.1.1 Scientific Events: Organization
General Chair, Scientific Chair
 Étienne André was a general chair of the 41st International Conference on Application and Theory of Petri Nets and Concurrency (Petri Nets 2020), that was organized virtually due to the COVID19 pandemic.
 Stephan Merz, together with Markus Kuppe and Leslie Lamport, chaired the TLA+Community Meeting, organized online as a satellite event of DISC 2020.
 Thomas Sturm was the chair of the steering committee of the International Symposium on Symbolic and Algebraic Computation (ISSAC), an ACM conference series.
Member of Organizing Committees
 Stephan Merz and Christoph Weidenbach are coorganizers of the International Summer School on Verification Techniques, Systems, and Applications (VTSA) that has been organized since 2008 in the Greater Region (Nancy, Saarbrücken, Luxembourg, Liège, and Koblenz). In 2020, VTSA had to be canceled due to the COVID19 pandemic.
 Christoph Weidenbach is a coorganizer of the final round of the German Computer Science Competition for High School Students (BWINF) that took place online in September 2020.
10.1.2 Scientific Events: Selection
Chair of Conference Program Committees
 Dominique Méry was cochair of the program committee of the 7th International Conference on Rigorous State Based Methods (ABZ 2020).
 Pascal Fontaine and Sophie Tourret were cochairs of the 7th Workshop on Practical Aspects of Automated Reasoning.
Member of Conference Program Committees
 Étienne André served on the program committees of the 25th International Conference on Engineering of Complex Computer Systems (ICECCS), the 22nd International Conference on Formal Engineering Methods (ICFEM), the 16th International Conference on integrated Formal Methods (iFM), the 25th IEEE Pacific Rim International Symposium on Dependable Computing (PRDC), and 14th International Symposium on Theoretical Aspects of Software Engineering (TASE).
 Pascal Fontaine served on the program committees of the 10th International Joint Conference on Automated Reasoning (IJCAR 2020), the 23rd International Conference on Theory and Applications of Satisfiability Testing (SAT), the 29th International Joint Conference on Artificial Intelligence (IJCAI 2020), and the 18th International Workshop on Satisfiability Modulo Theories (SMT).
 Dominique Méry served on the program committees of the 14th International Symposium of Theoretical Aspects of Software Engineering (TASE), the 17th International Colloquium on Theoretical Aspects of Computing (ICTAC), the 25th International Conference on Engineering of Complex Computer Systems (ICECCS), and the 22nd International Conference on Formal Engineering Methods (ICFEM).
 Stephan Merz served on the program committees of the International Conference on Rigorous State Based Methods (ABZ), the International Conference on Formal Techniques for Distributed Objects, Components, and Systems (FORTE), the 22nd International Conference on Formal Engineering Methods (ICFEM), the International Conference on Integrated Formal Methods (iFM), the International Conference on Tests and Proofs (TAP), and the International Workshop on Algebraic Development Techniques (WADT).
 Sorin Stratulat served on the program committees of the International Symposium on Symbolic and Numeric Algorithms for Scientific Computing (SYNASC), the International Conference on Information Assurance and Security (IAS), the Working Formal Methods Symposium (FROM), the International Conference on EUropean Transnational Educational (ICEUTE), and the International Conference on Computational Intelligence in Security for Information Systems (CISIS).
 Thomas Sturm was a member of the program committees of the 22nd Conference on Computer Algebra in Scientific Computing (CASC 2020) and the 5th International Workshop on Satisfiability Checking and Symbolic Computation (SCSquare 2020).
 Sophie Tourret was a member of the program committees of the 34th AAAI Conference on Artificial Intelligence (AAAI20) and the 29th International Joint Conference on Artificial Intelligence (IJCAI 2020).
 Uwe Waldmann was a member of the program committee of the 10th International Joint Conference on Automated Reasoning (IJCAR 2020).
 Christoph Weidenbach was a member of the program committee of the 10th International Joint Conference on Automated Reasoning (IJCAR 2020) and the 9th ACM SIGPLAN International Conference on Certified Programs and Proofs (CPP 2020).
10.1.3 Journals
Editorial Board Membership
 Thomas Sturm is an editor of the Journal of Symbolic Computation (Elsevier) since 2003 and an editor of Mathematics in Computer Science (Springer) since 2013.
 Christoph Weidenbach is a member of the editorial board of the Journal of Automated Reasoning (JAR) (Springer).
Special Issues Edited
 Thomas Sturm has edited a special issue of Mathematics in Computer Science on Computer Algebra in Scientific Computing47 and a special issue of the Journal of Symbolic Computation on Symbolic Computation and Satisfiability Checking46.
 Together with Armin Biere and Cesare Tinelli, Christoph Weidenbach edited the Journal of Automated Reasoning special issue Automated Reasoning Systems 14.
10.1.4 Invited Talks
Marie DuflotKremer gave a plenary invited talk at the DIDAPRO 8  DIDASTIC conference in Lille on February 7, 2020, on how to teach computer science without a computer.4
10.1.5 Leadership within the Scientific Community
 Stephan Merz is a member of the IFIP Working Group 2.2 on Formal Description of Programming Concepts.
 Christoph Weidenbach is president of CADE and a member of the IJCAR steering committee.
10.1.6 Scientific Expertise
 Étienne André was a scientific expert for the EIG CONCERTJapan (Japan Science and Technology Agency, 2020).
10.1.7 Research Administration
 Stephan Merz is the delegate for scientific affairs at the Inria Nancy – Grand Est research center and a member of Inria's Evaluation Committee. In 2020, he was a member of the hiring committees of senior researchers at Inria and of junior researchers at Inria Paris. He is also a member of the executive committee of the project on citizens' trust in the digital world (DigiTrust) funded by Lorraine Université d'Excellence.
 Thomas Sturm was an external expert on the appointment committee for a professorship “W2 Computeralgebra” at the University of Kassel, Germany.
 Sophie Tourret is the editor of the newsletter of AAR, the Association for Automated Reasoning.
 Uwe Waldmann is ombudsperson of the Max Planck Institute for Informatics.
 Christoph Weidenbach is a member of the selection committee of the Saarbrücken Graduate School in Computer Science. He was an external expert on the appointment committees for professorships in Oldenburg and Regensburg, Germany. He coordinates the scientific affairs at MPIINF.
10.2 Teaching  Supervision  Juries
10.2.1 Teaching
 DUT 1: Étienne André, Structures de données, 42 HETD, Université de Lorraine – IUT Charlemagne, France.
 DUT 1: Étienne André, Interfaces hommes machines, 57 HETD, Université de Lorraine – IUT Charlemagne, France.
 DUT 1: Étienne André, Architecture des réseaux, 32 HETD, Université de Lorraine – IUT Charlemagne, France.
 DUT 1: Étienne André, Conception orientée objets, 38 HETD, Université de Lorraine – IUT Charlemagne, France.
 DUT 2: Étienne André, Projets tuteurés, 14 HETD, Université de Lorraine – IUT Charlemagne, France.
 DUT 2: Étienne André, Stages, 42 HETD, Université de Lorraine – IUT Charlemagne, France.
 Licence: Marie DuflotKremer, Algorithmes et programmation 1, 60 HETD, L1, Université de Lorraine, France.
 Diplôme inter universitaire: Marie DuflotKremer, formation d'enseignants du secondaire à la spécialité NSI, 40 HETD, Université de Lorraine, France
 Licence: Marie DuflotKremer, Introduction au Web, 20 HETD, L1, Université de Lorraine, France
 Licence: Marie DuflotKremer, Accompagnement Algorithmique, 60 HETD, L1, Université de Lorraine, France
 Master: Marie DuflotKremer and Stephan Merz, Elements of model checking, 40 HETD, M2 Informatique and Master Erasmus Mundus DESEM, Université de Lorraine, France.
 Master: Marie DuflotKremer and Stephan Merz, Algorithmes distribués, 24 HETD M1 informatique, Université de Lorraine, France.
 Master: Dominique Méry, Modeling software systems, 30 HETD, M2, Université de Lorraine, France.
 Master: Dominique Méry, Modèles et algorithmes, 30 HETD, Université de Lorraine – Télécom Nancy, France.
 Master: Uwe Waldmann and Christoph Weidenbach, Automated Reasoning I, Universität des Saarlandes, Germany.
 Master: Uwe Waldmann, Automated Reasoning II, Universität des Saarlandes, Germany.
 Master: Markus Blaeser, Karl Bringmann, and Christoph Weidenbach, Competitive Programming, Universität des Saarlandes, Germany.
10.2.2 Supervision
 PhD: Margaux Duroeulx, SAT Techniques for Reliability Assessment, Université de Lorraine. Supervised by Nicolae Brînzei, Marie DuflotKremer, and Stephan Merz, 5 March 2020.
 PhD: Mathias Fleury, Formalization of Logical Calculi in Isabelle/HOL, Universität des Saarlandes. Supervised by Jasmin Blanchette and Christoph Weidenbach, 28 January 2020.
 PhD in progress: Antoine Defourné, SMT for TLAPS, Université de Lorraine. Supervised by Jasmin Blanchette, Pascal Fontaine, and Stephan Merz, since March 2019.
 PhD in progress: Daniel El Ouraoui, HigherOrder SMT, Université de Lorraine. Supervised by Jasmin Blanchette, Pascal Fontaine, and Stephan Merz, since November 2017.
 PhD in progress: Alexis Grall, Integration of a modeling language and a language for programming distributed systems, Université de Lorraine. Supervised by Horatiu Cirstea and Dominique Méry, since October 2018. Abandoned in September 2020.
 PhD in progress: Fajar Haifani, Explications in Logic, Universität des Saarlandes. Supervised by Christoph Weidenbach, since November 2019.
 PhD in progress: Dylan Marinho, Detecting timing attacks using formal methods, Université de Lorraine. Supervised by Étienne André, since October 2020.
 PhD in progress: Pierre Lermusiaux, Analysis of properties of interactive critical systems, Université de Lorraine. Supervised by Horatiu Cirstea and PierreEtienne Moreau, since October 2017.
 PhD in progress: HansJörg Schurr, HigherOrder SMT, Université de Lorraine. Supervised by Jasmin Blanchette, Pascal Fontaine, and Stephan Merz, since November 2017.
10.2.3 Juries
 Étienne André served as a reviewer in the PhD committees of Clément Bertrand (Université d’Evry, Université ParisSaclay), Victor Roussanaly (Université de Rennes 1), and Jiao Jiao (Nanyang Technological University, Singapore).
 Stephan Merz served as a reviewer in the PhD committees of Ivana Vukotic (University of Luxembourg) and of Xiaojie Guo (Université Grenoble Alpes).
 Pascal Fontaine served as a reviewer in the PhD committee of Yanis Sellami (Université Grenoble Alpes).
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. She is also a member of the CAPES NSI (numérique et sciences informatique) jury, the committee for hiring secondary school teachers.
 Christoph Weidenbach is the head of the steering committee of the German
Computer Science Competitions for pupils and high school students (BWINF)
https://
bwinf. .de/
10.3.2 Articles and contents
 Marie DuflotKremer is a member of the ERASMUS+ project PIAF with colleagues from Liège, Luxembourg, and Saarbrücken. This projects aims at studying how computational thinking can be introduced in primary education (with kids ranging from 5 to 12 years old). A catalogue of computational thinking competences has been designed, and test educational scenarios and didactical resources are being developed. This work was presented at the Didapro conference 32.
 As a member of the group Informatique Sans Ordinateur (ISO), Marie DuflotKremer takes part in creating new popularization activities and publishing online documentation to help people reproduce unplugged computer science activities. She also supervised two internships for 3rd year students to develop, test in classrooms and promote such activities.
10.3.3 Education
Marie DuflotKremer intervenes in the training of teachers. In 2020 she participated in two webinars for Educode.be.
10.3.4 Interventions
Marie DuflotKremer takes part every year in several local or national popularization events. In 2020 she contributed:
 a webinar for “confine ta science” during the lockdown in spring,
 a conference on computer networks for the event “filles, mathématiques et informatique, une équation lumineuse”, meant to promote mathematics and computer science towards high school girls,
 a presentation on the inaugural day of the “Chiche – 1 scientist 1 class” Inria project, intending to help high school students imagine their future in (computer) science.
11 Scientific production
11.1 Major publications
 1 inproceedingsveriT: an open, trustable and efficient SMTsolverProc. Conference on Automated Deduction (CADE)5663Lecture Notes in Computer ScienceMontreal, CanadaSpringer2009, 151156
 2 articleA complete and terminating approach to linear integer solvingJournal of Symbolic Computation100September 2020, 102136
 3 incollectionThe EventB Modelling Method  Concepts and Case StudiesLogics of Specification LanguagesMonographs in Theoretical Computer ScienceSpringerFebruary 2008, 33140
 4 inproceedingsTLA+ Proofs18th International Symposium On Formal Methods  FM 20127436Lecture Notes in Computer ScienceParis, FranceSpringer2012, 147154
 5 articleRedlog: Computer algebra meets computer logicACM SIGSAM Bull.3121997, 29
 6 articleDetection of Hopf bifurcations in chemical reaction networks using convex coordinatesJournal of Computational Physics291March 2015, 279  302
 7 articleSuperposition Decides the FirstOrder Logic Fragment Over Ground TheoriesMathematics 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 eliminationProc. ISSAC 2011San Jose, United StatesACM PressJune 2011, 329
 10 inproceedingsSPASS Version 3.522nd International Conference on Automated Deduction (CADE22)5663LNAIMontreal, CanadaSpringer2009, 140145
11.2 Publications of the year
International journals
 11 article Language Preservation Problems in Parametric Timed Automata Logical Methods in Computer Science 16 1 January 2020
 12 article Automated synthesis of local time requirement for service composition Software and Systems Modeling March 2020
 13 articleScalable FineGrained Proofs for Formula ProcessingJournal of Automated Reasoning643March 2020, 485510
 14 articlePreface to the Special Issue on Automated Reasoning SystemsJournal of Automated Reasoning643March 2020, 361362
 15 articleIdentifying the parametric occurrence of multiple steady states for some biological networksJournal of Symbolic Computation98May 2020, 84119
 16 articleA complete and terminating approach to linear integer solvingJournal of Symbolic Computation100September 2020, 102136
 17 articlePoliteness and Combination Methods for Theories with Bridging FunctionsJournal of Automated Reasoning642020, 97134
 18 articleLogical reduction of metarulesMachine Learning10972020, 1323  1369
 19 articleSymbolic computation and satisfiability checkingJournal of Symbolic Computation100September 2020, 110
 20 article Certified numerical algorithm for isolating the singularities of the plane projection of generic smooth space curves Journal of Computational and Applied Mathematics 2021
 21 articleFormalizing Bachmair and Ganzinger’s Ordered Resolution ProverJournal of Automated Reasoning647October 2020, 11691195
 22 articleSPASSAR: A FirstOrder Theorem Prover Based on ApproximationRefinement into the Monadic Shallow Linear FragmentJournal of Automated Reasoning643March 2020, 611640
International peerreviewed conferences
 23 inproceedings Parametric noninterference in timed automata Proceedings of the 25th International Conference on Engineering of Complex Computer Systems (ICECCS 2020) ICECCS 2020  25th International Conference on Engineering of Complex Computer Systems IEEE Conference Proceedings Singapore, Singapore https://formalanalysis.com/iceccs/2020/ March 2021
 24 inproceedings PIAF: promoting computational thinking and algorithmics in fundamental education Didapro 8 – DidaSTIC – L'informatique, objets d’enseignements – enjeux épistémologiques, didactiques et de formation Actes de la 8e édition du colloque Didapro  DidaSTIC Lille, France February 2020
 25 inproceedingsGenerating Distributed Programs from EventB ModelsInternational Workshop on Verification and Program Transformation320Dublin, IrelandAugust 2020, 110124
 26 inproceedings Pattern eliminating transformations LOPSTR 2020  30th International Symposium on LogicBased Program Synthesis and Transformation Bologna, Italy September 2020
 27 inproceedings Statistical Model Checking of Distributed Programs within SimGrid Proceedings of the 10th International Conference on Simulation and Modeling Methodologies, Technologies and Applications, SIMULTECH 2020 SIMULTECH 2020  10th International Conference on Simulation and Modeling Methodologies, Technologies and Applications Lieusaint, France July 2020
 28 inproceedings Towards Dynamic Dependable Systems through EvidenceBased Continuous Certification ISoLA 2020  9th International Symposium On Leveraging Applications of Formal Methods, Verification and Validation Rhodes, Greece October 2021
 29 inproceedingsGuaranteed phase synchronization of hybrid oscillators using symbolic Euler's method (verification challenge)Proceedings of the 7th International Workshop on Applied Verification of Continuous and Hybrid Systems (ARCH 2020)ARCH20  7th International Workshop on Applied Verification of Continuous and Hybrid SystemsEPiC Series in ComputingProceedings of the 7th International Workshop on Applied Verification of Continuous and Hybrid Systems (ARCH 2020)74Berlin, Germanyhttps://cpsvo.org/group/ARCHSeptember 2020, 197184
 30 inproceedingsSignatureBased Abduction for Expressive Description Logics17th International Conference on Principles of Knowledge Representation and Reasoning {KR2020}Proceedings of the 17th International Conference on Principles of Knowledge Representation and ReasoningRhodes, FranceSeptember 2020, 592602
 31 inproceedingsAn Integrated Framework for the Formal Analysis of Critical Interactive SystemsThe 27th AsiaPacific Software Engineering ConferenceThe 27th AsiaPacific Software Engineering ConferenceSingapour, Singaporehttps://formalanalysis.com/apsec/2020/December 2020, 10
 32 inproceedingsPIAF: Developing Computational and Algorithmic Thinking in Fundamental EducationAACE 2020  EdMedia + Innovate Learning1Proceedings of EdMedia + Innovate Learning 2020 OnlineAmsterdam / Virtual, Netherlandshttp://www.aace.org/conf/edmedia/2020, 315322
 33 inproceedingsBest paperPoliteness for the Theory of Algebraic Datatypes10th International Joint Conference on Automated Reasoning, IJCAR12166Lecture Notes in Computer ScienceParis, France2020, 238255
 34 inproceedingsSPIKE, an automatic theorem prover  revisitedSYNASC2020 22nd International Symposium on Symbolic and Numeric Algorithms for Scientific ComputingInternational Symposium on Symbolic and Numeric Algorithms for Scientific ComputingTimisoara, RomaniaSeptember 2020, 9396
 35 inproceedingsA Comprehensive Framework for Saturation Theorem ProvingIJCAR 2020 (Part I) International Joint Conference on Automated Reasoning12166IJCAR 2020: Automated ReasoningParis, FranceJune 2020, 316334
Conferences without proceedings
 36 inproceedings An Extension of PlusCal for Modeling Distributed Algorithms TLA+ Community Event 2020 Freiburg (online), Germany October 2020
 37 inproceedings Better Automation for TLA+ Proofs TLA+ Community Event 2020 Virtual, France https://conf.tlapl.us/home/ October 2020
 38 inproceedings Higherorder Automation in TLAPS JFLA 2020  31emes Journées Francophones des Langages Applicatifs Gruissan, France http://jfla.inria.fr/jfla2020.html January 2020
 39 inproceedings On a Notion of Relevance Proceedings of the 33rd International Workshop on Description Logics (DL 2020) Online, Greece September 2020
 40 inproceedings A Graph Theoretical Approach for Testing Binomiality of Reversible Chemical Reaction Networks 22nd International Symposium on Symbolic and Numeric Algorithms for Scientific Computing  SYNASC 2020 Timisoara/Virtual, Romania https://synasc.ro/2020/ September 2020
 41 inproceedings Lifting congruence closure with free variables to λfree higherorder logic via SAT encoding SMT 2020  18th International Workshop on Satisfiability Modulo Theories Online COVID19, France July 2020
Scientific book chapters
 42 inbookA Linear Algebra Approach for Detecting Binomiality of Steady State Ideals of Reversible Chemical Reaction NetworksComputer Algebra in Scientific Computing: 22nd International Workshop  CASC 2020October 2020, 492509
 43 inbookFirstOrder Tests for Toricity12291Computer Algebra in Scientific Computing, CASC 2020October 2020, 510527
 44 inbookA Mission Definition, Verification and Validation Architecture12232Formal Methods. FM 2019 International WorkshopsAugust 2020, 281287
Edition (books, proceedings, special issue of a journal)
 45 book Implicit and Explicit Semantics Integration in ProofBased Developments of Discrete Systems 2021
 46 book Special Issue : Symbolic Computation and Satisfiability Checking Journal of Symbolic Computation 100 September 2020
 47 proceedings M. England W. Koepf T. Sadykov W. Seiler T. Sturm Special Issue: Proceedings of the 21st International Workshop on Computer Algebra in Scientific Computing (CASC 2019) Moscow, Russia 2021
 48 proceedings A. Raschke D. Méry F. Houdek Rigorous StateBased Methods  7th International Conference, {ABZ} 2020, Ulm, Germany, May 2729, 2020, Proceedings ABZ 2020 Lecture Notes in Computer Science Rigorous StateBased Methods  7th International Conference, {ABZ} 2020, Ulm, Germany, May 2729, 2020, Proceedings ULM, Germany May 2020
Doctoral dissertations and habilitation theses
 49 thesis Reliability assessment of systems modeled by fault trees thanks to satisfiability techniques Université de Lorraine March 2020
 50 thesis Formalization of Logical Calculi in Isabelle/HOL Universität des Saarlandes Saarbrücken January 2020
Reports & preprints
 51 misc SCL with Theory Constraints October 2020
 52 report A Refinement Strategy for Hybrid System Design with Safety Constraints Université de Lorraine; INRIA; CNRS July 2020
 53 reportGenerating Distributed Programs from EventB ModelsLORIA UMR 7503 CNRS, INRIA, Université de LORRAINEMay 2020, 36
 54 misc Algorithmic Reduction of Biological Networks With Multiple Time Scales October 2020
 55 misc A Linear Algebra Approach for Detecting Binomiality of Steady State Ideals of Reversible Chemical Reaction Networks February 2020
 56 misc FirstOrder Tests for Toricity February 2020
 57 misc A Logic Based Approach to Finding Real Singularities of Implicit Ordinary Differential Equations March 2020
 58 misc ECyclist: Implementation of an Efficient Validation of FOL ID Cyclic Induction Reasoning (System Description) February 2020
11.3 Cited publications
 59 articleThe Existence of Refinement MappingsTheoretical Computer Science812May 1991, 253284
 60 book Modeling in EventB: System and Software Engineering Cambridge University Press 2010
 61 inproceedingsParametric realtime reasoningProc. 25th Annual ACM Symp. Theory of ComputingSan Diego, CA, USAACM1993, 592601
 62 articleRewriteBased Equational Theorem Proving with Selection and SimplificationJournal of Logic and Computation431994, 217247
 63 book Refinement calculusA systematic introduction Springer Verlag 1998
 64 inproceedingsExtending SMT Solvers to HigherOrder LogicCADE2711716Lecture Notes in Computer ScienceNatal, BrazilSpringerAugust 2019, 3554
 65 incollectionSatisfiability Modulo TheoriesHandbook of Satisfiability185Frontiers in Artificial Intelligence and ApplicationsIOS PressFebruary 2009, 26825885
 66 articleWhat you Always Wanted to Know About Datalog (And Never Dared to Ask)IEEE Trans. Knowl. Data Eng.11March 1989, 146166
 67 inproceedingsA Polite NonDisjoint Combination Method: Theories with Bridging Functions Revisited25th International Conference on Automated Deduction, CADE259195Lecture Notes in Computer ScienceChristoph BenzmuellerBerlin, GermanySpringerAugust 2015, 419433
 68 inproceedingsA Rewriting Approach to the Combination of Data Structures with Bridging TheoriesFrontiers of Combining Systems  10th International Symposium, FroCoS 20159322Lecture Notes in Computer ScienceWroclaw, PolandSpringerSeptember 2015, 275290
 69 inproceedingsReconstructing veriT Proofs in Isabelle/HOLPxTP 2019  Sixth Workshop on Proof eXchange for Theorem Proving301https://arxiv.org/abs/1908.09480Natal, BrazilAugust 2019, 3650
 70 unpublishedEfficiently and Effectively Recognizing Toricity of Steady State VarietiesOctober 2019, working paper or preprint
 71 book Specifying Systems Boston, Mass. AddisonWesley 2002
 72 inproceedingsThe PlusCal Algorithm Language6th Intl. Coll. Theoretical Aspects of Computing (ICTAC 2009)5684Lecture Notes in Computer ScienceKuala Lumpur, MalaysiaSpringer2009, 3660
 73 booklet Singularities of Algebraic Differential Equations Preprint Kassel University (arXiv:2002.11597) 2020
 74 articleBioModels Database: A Free, Centralized Database of Curated, Published, Quantitative Kinetic Models of Biochemical and Cellular SystemsNucleic acids res.34suppl_1January 2006, D689D691
 75 articleTransmission Dynamics and Control Strategies Assessment of Avian Influenza A (H5N6) in the PhilippinesInfectious Disease Modelling32018, 3559
 76 book Programming from Specifications 2nd edition Prentice Hall 1998
 77 phdthesis Decidable fragments of firstorder logic and of firstorder linear arithmetic with uninterpreted predicates Saarland University, Saarbrücken, Germany 2019