2023Activity reportProject-TeamANTIQUE

RNSR: 201421111R
  • Research center Inria Paris Centre
  • In partnership with:CNRS, Ecole normale supérieure de Paris
  • Team name: Static Analysis by Abstract Interpretation
  • In collaboration with:Département d'Informatique de l'Ecole Normale Supérieure
  • Domain:Algorithmics, Programming, Software and Architecture
  • Theme:Proofs and Verification


Computer Science and Digital Science

  • A2. Software
  • A2.1. Programming Languages
  • A2.1.1. Semantics of programming languages
  • A2.1.7. Distributed programming
  • A2.1.12. Dynamic languages
  • A2.2.1. Static analysis
  • A2.3. Embedded and cyber-physical systems
  • A2.3.1. Embedded systems
  • A2.3.2. Cyber-physical systems
  • A2.3.3. Real-time systems
  • A2.4. Formal method for verification, reliability, certification
  • A2.4.1. Analysis
  • A2.4.2. Model-checking
  • A2.4.3. Proofs
  • A2.6.1. Operating systems
  • A4.4. Security of equipment and software
  • A4.5. Formal methods for security

Other Research Topics and Application Domains

  • B1.1. Biology
  • B1.1.8. Mathematical biology
  • B1.1.10. Systems and synthetic biology
  • B5.2. Design and manufacturing
  • B5.2.1. Road vehicles
  • B5.2.2. Railway
  • B5.2.3. Aviation
  • B5.2.4. Aerospace
  • B6.1. Software industry
  • B6.1.1. Software engineering
  • B6.1.2. Software evolution, maintenance
  • B6.6. Embedded systems

1 Team members, visitors, external collaborators

Research Scientists

  • Xavier Rival [Team leader, INRIA, Senior Researcher, HDR]
  • Bernadette Charron-Bost [CNRS, Senior Researcher, HDR]
  • Vincent Danos [CNRS, Senior Researcher, HDR]
  • Jerome Feret [INRIA, Researcher, HDR]
  • Caterina Urban [INRIA, Researcher]

Post-Doctoral Fellows

  • Matthieu Bouguéon [ENS, from Sep 2023]
  • Marco Campion [INRIA, Post-Doctoral Fellow, from Feb 2023]
  • Alessandro De Palma [INRIA, Post-Doctoral Fellow, from Nov 2023]
  • Adam Khayam [INRIA, Post-Doctoral Fellow]

PhD Students

  • Jerome Boillot [ENS PARIS]
  • Serge Durand [CEA]
  • Josselin Giet [INRIA, from Sep 2023]
  • Josselin Giet [ENS PARIS, until Aug 2023]
  • Patricio Inzaghi [INRIA, until Aug 2023]
  • Denis Mazzucato [INRIA]
  • Naim Moussaoui Remil [INRIA, from Nov 2023]
  • Louis Penet De Monterno [ECOLE POLY PALAISEAU, until Sep 2023]
  • Albin Salazar [INRIA, until Aug 2023]
  • Ignacio Tiraboschi [INRIA]

Technical Staff

  • Antoine Pouille [INRIA, Engineer, from Oct 2023]

Interns and Apprentices

  • Charles De Haro [ENS RENNES, Intern, from Mar 2023 until Aug 2023]
  • Naim Moussaoui Remil [UNIV PARIS - CITE, Intern, from Mar 2023 until Aug 2023]
  • Abhinandan Pal [INRIA, Intern, until Jan 2023]
  • Kevin Pinochet Hernandez [INRIA, Intern, until Apr 2023]
  • Orphee Radet [INRIA, Intern, until May 2023]

Administrative Assistants

  • Meriem Guemair [INRIA]
  • Diana Marino Duarte [INRIA, from Mar 2023]

2 Overall objectives

Our group focuses on developing automated techniques to compute semantic properties of programs and other systems with a computational semantics in general. Such properties include (but are not limited to) important classes of correctness properties.

Verifying safety critical systems (such as avionics systems) is an important motivation to compute such properties. Indeed, a fault in an avionics system, such as a runtime error in the fly-by-wire command software, may cause an accident, with loss of life. As these systems are also very complex and are developed by large teams and maintained over long periods, their verification has become a crucial challenge. Safety critical systems are not limited to avionics: software runtime errors in cruise control management systems were recently blamed for causing unintended acceleration in certain Toyota models (the case was settled with a 1.2 billion dollars fine in March 2014, after years of investigation and several trials). Similarly, other transportation systems (railway), energy production systems (nuclear power plants, power grid management), medical systems (pacemakers, surgery and patient monitoring systems), and value transfers in decentralized systems (smart contracts), rely on complex software, which should be verified.

Beyond the field of embedded systems, other pieces of software may cause very significant harm in the case of bugs, as demonstrated by the Heartbleed security hole: due to a wrong protocol implementation, many websites could leak private information, over years.

An important example of semantic properties is the class of safety properties. A safety property typically specifies that some (undesirable) event will never occur, whatever the execution of the program that is considered. For instance, the absence of runtime error is a very important safety property. Other important classes of semantic properties include liveness properties (i.e., properties that specify that some desirable event will eventually occur) such as termination and security properties, such as the absence of information flows from private to public channels.

All these software semantic properties are not decidable, as can be shown by reduction to the halting problem. Therefore, there is no chance to develop any fully automatic technique able to decide, for any system, whether or not it satisfies some given semantic property.

The classic development techniques used in industry involve testing, which is not sound, as it only gives information about a usually limited test sample: even after successful test-based validation, situations that were untested may generate a problem. Furthermore, testing is costly in the long term, as it should be re-done whenever the system to verify is modified. Machine-assisted verification is another approach which verifies human specified properties. However, this approach also presents a very significant cost, as the annotations required to verify large industrial applications would be huge.

By contrast, the antique group focuses on the design of semantic analysis techniques that should be sound (i.e., compute semantic properties that are satisfied by all executions) and automatic (i.e., with no human interaction), although generally incomplete (i.e., not able to compute the best —in the sense of: most precise— semantic property). As a consequence of incompleteness, we may fail to verify a system that is actually correct. For instance, in the case of verification of absence of runtime error, the analysis may fail to validate a program, which is safe, and emit false alarms (that is reports that possibly dangerous operations were not proved safe), which need to be discharged manually. Even in this case, the analysis provides information about the alarm context, which may help disprove it manually or refine the analysis.

The methods developed by the antique group are not limited to the analysis of software. We also consider complex biological systems (such as models of signaling pathways, i.e. cascades of protein interactions, which enable signal communication among and within cells), described in higher level languages, and use abstraction techniques to reduce their combinatorial complexity and capture key properties so as to get a better insight in the underlying mechanisms of these systems.

3 Research program

3.1 Semantics

Semantics plays a central role in verification since it always serves as a basis to express the properties of interest, that need to be verified, but also additional properties, required to prove the properties of interest, or which may make the design of static analysis easier.

For instance, if we aim for a static analysis that should prove the absence of runtime error in some class of programs, the concrete semantics should define properly what error states and non error states are, and how program executions step from a state to the next one. In the case of a language like C, this includes the behavior of floating point operations as defined in the IEEE 754 standard. When considering parallel programs, this includes a model of the scheduler, and a formalization of the memory model.

In addition to the properties that are required to express the proof of the property of interest, it may also be desirable that semantics describe program behaviors in a finer manner, so as to make static analyses easier to design. For instance, it is well known that, when a state property (such as the absence of runtime error) is valid, it can be established using only a state invariant (i.e., an invariant that ignores the order in which states are visited during program executions). Yet searching for trace invariants (i.e., that take into account some properties of program execution history) may make the static analysis significantly easier, as it will allow it to make finer case splits, directed by the history of program executions. To allow for such powerful static analyses, we often resort to a non standard semantics, which incorporates properties that would normally be left out of the concrete semantics.

3.2 Abstract interpretation and static analysis

Once a reference semantics has been fixed and a property of interest has been formalized, the definition of a static analysis requires the choice of an abstraction. The abstraction ties a set of abstract predicates to the concrete ones, which they denote. This relation is often expressed with a concretization function that maps each abstract element to the concrete property it stands for. Obviously, a well chosen abstraction should allow one to express the property of interest, as well as all the intermediate properties that are required in order to prove it (otherwise, the analysis would have no chance to achieve a successful verification). It should also lend itself to an efficient implementation, with efficient data-structures and algorithms for the representation and the manipulation of abstract predicates. A great number of abstractions have been proposed for all kinds of concrete data types, yet the search for new abstractions is a very important topic in static analysis, so as to target novel kinds of properties, to design more efficient or more precise static analyses.

Once an abstraction is chosen, a set of sound abstract transformers can be derived from the concrete semantics and that account for individual program steps, in the abstract level and without forgetting any concrete behavior. A static analysis follows as a result of this step by step approximation of the concrete semantics, when the abstract transformers are all computable. This process defines an abstract interpretation  35. The case of loops requires a bit more work as the concrete semantics typically relies on a fixpoint that may not be computable in finitely many iterations. To achieve a terminating analysis we then use widening operators  35, which over-approximate the concrete union and ensure termination.

A static analysis defined that way always terminates and produces sound over-approximations of the programs behaviors. Yet, these results may not be precise enough for verification. This is where the art of static analysis design comes into play through, among others:

  • the use of more precise, yet still efficient enough abstract domains;
  • the combination of application-specific abstract domains;
  • the careful choice of abstract transformers and widening operators.

3.3 Applications of the notion of abstraction in semantics

In the previous subsections, we sketched the steps in the design of a static analyzer to infer some family of properties, which should be implementable, and efficient enough to succeed in verifying non trivial systems.

The same principles can be applied successfully to other goals. In particular, the abstract interpretation framework should be viewed as a very general tool to compare different semantics, not necessarily with the goal of deriving a static analyzer. Such comparisons may be used in order to prove two semantics equivalent (i.e., one is an abstraction of the other and vice versa), or that a first semantics is strictly more expressive than another one (i.e., the latter can be viewed an abstraction of the former, where the abstraction actually makes some information redundant, which cannot be recovered). A classical example of such comparison is the classification of semantics of transition systems  34, which provides a better understanding of program semantics in general. For instance, this approach can be applied to get a better understanding of the semantics of a programming language, but also to select which concrete semantics should be used as a foundation for a static analysis, or to prove the correctness of a program transformation, compilation or optimization.

3.4 From properties to explanations

In many application domains, we can go beyond the proof that a program satisfies its specification. Abstractions can also offer new perspectives to understand how complex behaviors of programs emerge from simpler computation steps. Abstractions can be used to find compact and readable representations of sets of traces, causal relations, and even proofs. For instance, abstractions may decipher how the collective behaviors of agents emerge from the orchestration of their individual ones in distributed systems (such as consensus protocols, models of signaling pathways). Another application is the assistance for the diagnostic of alarms of a static analyzer.

Complex systems and software have often times intricate behaviors, leading to executions that are hard to understand for programmers and also difficult to reason about with static analyzers. Shared memory and distributed systems are notorious for being hard to reason about due to the interleaving of actions performed by different processes and the non-determinism of the network that might lose, corrupt, or duplicate messages. Reduction theorems, e.g., Lipton's theorem, have been proposed to facilitate reasoning about concurrency, typically transforming a system into one with a coarse-grained semantics that usually increases the atomic sections. We investigate reduction theorems for distributed systems and ways to compute the coarse-grained counter part of a system automatically. Compared with shared memory concurrency, automated methods to reason about distributed systems have been less investigated in the literature. We take a programming language approach based on high-level programming abstractions. We focus on partially-synchronous communication closed round-based models, introduced in the distributed algorithms community for its simpler proof arguments. The high-level language is compiled into a low-level (asynchronous) programming language. Conversely, systems defined under asynchronous programming paradigms are decompiled into the high-level programming abstractions. The correctness of the compilation/decompilation process is based on reduction theorems (in the spirit of Lipton and Elrad-Francez) that preserve safety and liveness properties.

In models of signaling pathways, collective behavior emerges from competition for common resources, separation of scales (time/concentration), non linear feedback loops, which are all consequences of mechanistic interactions between individual bio-molecules (e.g., proteins). While more and more details about mechanistic interactions are available in the literature, understanding the behavior of these models at the system level is far from easy. Causal analysis helps explaining how specific events of interest may occur. Model reduction techniques combine methods from different domains such as the analysis of information flow used in communication protocols, and tropicalization methods that comes from physics. The result is lower dimension systems that preserve the behavior of the initial system while focusing of the elements from which emerges the collective behavior of the system.

The abstraction of causal traces offer nice representation of scenarios that lead to expected or unexpected events. This is useful to understand the necessary steps in potential scenarios in signaling pathways; this is useful as well to understand the different steps of an intrusion in a protocol. Lastly, traces of computation of a static analyzer can themselves be abstracted, which provides assistance to classify true and false alarms. Abstracted traces are symbolic and compact representations of sets of counter-examples to the specification of a system which help one to either understand the origin of bugs, or to find that some information has been lost in the abstraction leading to false alarms.

4 Application domains

4.1 Verification of safety critical embedded software

The verification of safety critical embedded software is a very important application domain for our group. First, this field requires a high confidence in software, as a bug may cause disastrous events. Thus, it offers an obvious opportunity for a strong impact. Second, such software usually have better specifications and a better design than many other families of software, hence are an easier target for developing new static analysis techniques (which can later be extended for more general, harder to cope with families of programs). This includes avionics, automotive and other transportation systems, medical systems ...

For instance, the verification of avionics systems represent a very high percentage of the cost of an airplane (about 30 % of the overall airplane design cost). The state of the art development processes mainly resort to testing in order to improve the quality of software. Depending on the level of criticality of a software (at the highest levels, any software failure would endanger the flight) a set of software requirements are checked with test suites. This approach is both costly (due to the sheer amount of testing that needs to be performed) and unsound (as errors may go unnoticed, if they do not arise on the test suite).

By contrast, static analysis can ensure higher software quality at a lower cost. Indeed, a static analyzer will catch all bugs of a certain kind. Moreover, a static analysis run typically lasts a few hours, and can be integrated in the development cycle in a seamless manner. For instance, Astrée successfully verified the absence of runtime error in several families of safety critical fly-by-wire avionic software, in at most a day of computation, on standard hardware. Other kinds of synchronous embedded software have also been analyzed with good results.

In the future, we plan to greatly extend this work so as to verify other families of embedded software (such as communication, navigation and monitoring software) and other families of properties (such as security and liveness properties).

Embedded software in charge of communication, navigation, and monitoring typically relies on a parallel structure, where several threads are executed concurrently, and manage different features (input, output, user interface, internal computation, logging ...). This structure is also often found in automotive software. An even more complex case is that of distributed systems, where several separate computers are run in parallel and take care of several sub-tasks of a same feature, such as braking. Such a logical structure is not only more complex than the synchronous one, but it also introduces new risks and new families of errors (deadlocks, data-races...). Moreover, such less well designed, and more complex embedded software often utilizes more complex data-structures than synchronous programs (which typically only use arrays to store previous states) and may use dynamic memory allocation, or build dynamic structures inside static memory regions, which are actually even harder to verify than conventional dynamically allocated data structures. Complex data-structures also introduce new kinds of risks (the failure to maintain structural invariants may lead to runtime errors, non termination, or other software failures). To verify such programs, we will design additional abstract domains, and develop new static analysis techniques, in order to support the analysis of more complex programming language features such as parallel and concurrent programming with threads and manipulations of complex data structures. Due to their size and complexity, the verification of such families of embedded software is a major challenge for the research community.

Furthermore, embedded systems also give rise to novel security concerns. It is in particular the case for some aircraft-embedded computer systems, which communicate with the ground through untrusted communication media. Besides, the increasing demand for new capabilities, such as enhanced on-board connectivity, e.g. using mobile devices, together with the need for cost reduction, leads to more integrated and interconnected systems. For instance, modern aircrafts embed a large number of computer systems, from safety-critical cockpit avionics to passenger entertainment. Some systems meet both safety and security requirements. Despite thorough segregation of subsystems and networks, some shared communication resources raise the concern of possible intrusions. Because of the size of such systems, and considering that they are evolving entities, the only economically viable alternative is to perform automatic analyses. Such analyses of security and confidentiality properties have never been achieved on large-scale systems where security properties interact with other software properties, and even the mapping between high-level models of the systems and the large software base implementing them has never been done and represents a great challenge. Our goal is to prove empirically that the security of such large scale systems can be proved formally, thanks to the design of dedicated abstract interpreters.

The long term goal is to make static analysis more widely applicable to the verification of industrial software.

4.2 Static analysis of software components and libraries

An important goal of our work is to make static analysis techniques easier to apply to wider families of software. Then, in the longer term, we hope to be able to verify less critical, yet very commonly used pieces of software. Those are typically harder to analyze than critical software, as their development process tends to be less rigorous. In particular, we will target operating systems components and libraries. As of today, the verification of such programs is considered a major challenge to the static analysis community.

As an example, most programming languages offer Application Programming Interfaces (API) providing ready-to-use abstract data structures (e.g., sets, maps, stacks, queues, etc.). These APIs, are known under the name of containers or collections, and provide off-the-shelf libraries of high level operations, such as insertion, deletion and membership checks. These container libraries give software developers a way of abstracting from low-level implementation details related to memory management, such as dynamic allocation, deletion and pointer handling or concurrency aspects, such as thread synchronization. Libraries implementing data structures are important building bricks of a huge number of applications, therefore their verification is paramount. We are interested in developing static analysis techniques that will prove automatically the correctness of large audience libraries such as Glib and Threading Building Blocks.

4.3 Models of mechanistic interactions between proteins

Computer Science takes a more and more important role in the design and the understanding of biological systems such as signaling pathways, self assembly systems, DNA repair mechanisms. Biology has gathered large data-bases of facts about mechanistic interactions between proteins, but struggles to draw an overall picture of how these systems work as a whole. High level languages designed in Computer Science allow one to collect these interactions in integrative models, and provide formal definitions (i.e., semantics) for the behavior of these models. This way, modelers can encode their knowledge, following a bottom-up discipline, without simplifying a priori the models at the risk of damaging the key properties of the system. Yet, the systems that are obtained this way suffer from combinatorial explosion (in particular, in the number of different kinds of molecular components, which can arise at run-time), which prevents from a naive computation of their behavior.

We develop various analyses based on abstract interpretation, and tailored to different phases of the modeling process. We propose automatic static analyses in order to detect inconsistencies in the early phases of the modeling process. These analyses are similar to the analysis of classical safety properties of programs. They involve both forward and backward reachability analyses as well as causality analyses, and can be tuned at different levels of abstraction. We also develop automatic static analyses in order to identify key elements in the dynamics of these models. The results of these analyses are sent to another tool, which is used to automatically simplify models. The correctness of this simplification process is proved by the means of abstract interpretation: this ensures formally that the simplification preserves the quantitative properties that have been specified beforehand by the modeler. The whole pipeline is parameterized by a large choice of abstract domains which exploits different features of the high level description of models.

4.4 Consensus

Fault-tolerant distributed systems provide a dependable service on top of unreliable computers and networks. Famous examples are geo-replicated data-bases, distributed file systems, or blockchains. Fault-tolerant protocols replicate the system and ensure that all (unreliable) replicas are perceived from the outside as one single reliable machine. To give the illusion of a single reliable machine “consensus” protocols force replicas to agree on the “current state” before making this state visible to an outside observer. We are interested in (semi-)automatically proving the total correctness of consensus algorithms in the benign case (messages are lost or processes crash) or the Byzantine case (processes may lie about their current state). In order to do this, we first define new reduction theorems to simplify the behaviors of the system and, second, we introduce new static analysis methods to prove the total correctness of adequately simplified systems. We focus on static analysis based Satisfiability Modulo Theories (SMT) solvers which offers a good compromise between automation and expressiveness. Among our benchmarks are Paxos, PBFT (Practical Byzantine Fault-Tolerance), and blockchain algorithms (Red-Belly, Tendermint, Algorand). These are highly challenging benchmarks, with a lot of non-determinism coming from the interleaving semantics and from the adversarial environment in which correct processes execute, environment that can drop messages, corrupt them, etc. Moreover, these systems were originally designed for a few servers but today are deployed on networks with thousands of nodes. The “optimizations” for scalability can no longer be overlooked and must be considered as integral part of the algorithms, potentially leading to specifications weaker than the so much desired consensus.

4.5 Smart contracts

Blockchain applications in finance have emerged in 2020 as the lead applications. The new field called decentralised finance (or also open finance) re-creates basic financial functionalities such as ireeversible and reverible swaps of assets. There are broad goals to our research in this emerging area: structuring contract languages which guarantee good execution properties by construction, and finding mechanisms that foster liquidity.

We are investigating several other problems in decentralised finance: protocols for capital-efficient decentralised exchanges; general convex problems for the optimal routing and arbitrage in the network of exchange platforms; and the economics of the competition between two-sided exchange platforms.

4.6 Static analysis of data science software

Nowadays, thanks to advances in machine learning and the availability of vast amounts of data, computer software plays an increasingly important role in assisting or even autonomously performing tasks in our daily lives. As data science software becomes more and more widespread, we become increasingly vulnerable to programming errors. In particular, programming errors that do not cause failures can have serious consequences since code that produces an erroneous but plausible result gives no indication that something went wrong. This issue becomes particularly worrying knowing that machine learning software, thanks to its ability to efficiently approximate or simulate more complex systems, is slowly creeping into mission critical scenarios. However, programming errors are not the only concern. Another important issue is the vulnerability of machine learning models to adversarial examples, that is, small input perturbations that cause the model to misbehave in unpredictable ways. More generally, a critical issue is the notorious difficulty to interpret and explain machine learning software. Finally, as we are witnessing widespread adoption of software with far-reaching societal impact — i.e., to automate decision-making in fields such as social welfare, criminal justice, and even health care — a number of recent cases have evidenced the importance of ensuring software fairness as well as data privacy. Going forward, data science software will be subject to more and more legal regulations (e.g., the European General Data Protection Regulation adopted in 2016) as well as administrative audits.

It is thus paramount to develop method and tools that can keep up with these developments and enhance our understanding of data science software and ensure it behaves correctly and reliably. In particular, we are interesting in developing new static analyses specifically tailored to the idiosyncrasies of data science software. This makes it a new and exciting area for static analysis, offering a wide variety of challenging problems with huge potential impact on various interdisciplinary application domains 38.

5 Social and environmental responsibility

5.1 Impact of research results

We are advising several companies such as Bender operating on the Tezos blockchain, think tanks such as the CDC Labchain (Caisse des Dépots), and other informal development groups such as Jaxnet on decentralised finance protocols and mechanism design for consensus incentives.

We are advising static analysis companies including AbsInt Angewandte Informatik (static analysis for the verification of embedded software) and MatrixLead (static analysis for spreadsheet applications).

6 Highlights of the year

  • Jérôme Boillot was a member of the team Mopsa who won the Gold Medal (Winner) of SV-Comp's SoftwareSystems category 2024. The competition will take place at TACAS. The detailed results are available here.
  • Josselin Giet and Félix Ridoux received the Radhia Cousot Award for the best student paper at SAS 2023. The details are available here.

7 New software, platforms, open data

7.1 New software

7.1.1 APRON

  • Scientific Description:
    The APRON library is intended to be a common interface to various underlying libraries/abstract domains and to provide additional services that can be implemented independently from the underlying library/abstract domain, as shown by the poster on the right (presented at the SAS 2007 conference. You may also look at:
  • Functional Description:
    The Apron library is dedicated to the static analysis of the numerical variables of a program by abstract interpretation. Its goal is threefold: provide ready-to-use numerical abstractions under a common API for analysis implementers, encourage the research in numerical abstract domains by providing a platform for integration and comparison of domains, and provide a teaching and demonstration tool to disseminate knowledge on abstract interpretation.
  • URL:
  • Contact:
    Antoine Miné
  • Participants:
    Antoine Miné, Bertrand Jeannet

7.1.2 Astrée

  • Name:
    The AstréeA Static Analyzer of Asynchronous Software
  • Keywords:
    Static analysis, Static program analysis, Program verification, Software Verification, Abstraction
  • Scientific Description:

    Astrée analyzes structured C programs, with complex memory usages, but without dynamic memory allocation nor recursion. This encompasses many embedded programs as found in earth transportation, nuclear energy, medical instrumentation, and aerospace applications, in particular synchronous control/command. The whole analysis process is entirely automatic.

    Astrée discovers all runtime errors including:

    undefined behaviors in the terms of the ANSI C99 norm of the C language (such as division by 0 or out of bounds array indexing),

    any violation of the implementation-specific behavior as defined in the relevant Application Binary Interface (such as the size of integers and arithmetic overflows),

    any potentially harmful or incorrect use of C violating optional user-defined programming guidelines (such as no modular arithmetic for integers, even though this might be the hardware choice),

    failure of user-defined assertions.

  • Functional Description:

    Astrée analyzes structured C programs, with complex memory usages, but without dynamic memory allocation nor recursion. This encompasses many embedded programs as found in earth transportation, nuclear energy, medical instrumentation, and aerospace applications, in particular synchronous control/command. The whole analysis process is entirely automatic.

    Astrée discovers all runtime errors including: - undefined behaviors in the terms of the ANSI C99 norm of the C language (such as division by 0 or out of bounds array indexing), - any violation of the implementation-specific behavior as defined in the relevant Application Binary Interface (such as the size of integers and arithmetic overflows), - any potentially harmful or incorrect use of C violating optional user-defined programming guidelines (such as no modular arithmetic for integers, even though this might be the hardware choice), - failure of user-defined assertions.

    Astrée is a static analyzer for sequential programs based on abstract interpretation. The Astrée static analyzer aims at proving the absence of runtime errors in programs written in the C programming language.

  • URL:
  • Contact:
    Patrick Cousot
  • Participants:
    Antoine Miné, Jerome Feret, Laurent Mauborgne, Patrick Cousot, Radhia Cousot, Xavier Rival
  • Partners:
    CNRS, ENS Paris, AbsInt Angewandte Informatik GmbH

7.1.3 AstréeA

  • Name:
    The AstréeA Static Analyzer of Asynchronous Software
  • Keywords:
    Static analysis, Static program analysis
  • Scientific Description:
    AstréeA analyzes C programs composed of a fixed set of threads that communicate through a shared memory and synchronization primitives (mutexes, FIFOs, blackboards, etc.), but without recursion nor dynamic creation of memory, threads nor synchronization objects. AstréeA assumes a real-time scheduler, where thread scheduling strictly obeys the fixed priority of threads. Our model follows the ARINC 653 OS specification used in embedded industrial aeronautic software. Additionally, AstréeA employs a weakly-consistent memory semantics to model memory accesses not protected by a mutex, in order to take into account soundly hardware and compiler-level program transformations (such as optimizations). AstréeA checks for the same run-time errors as Astrée , with the addition of data-races.
  • Functional Description:
    AstréeA is a static analyzer prototype for parallel software based on abstract interpretation. The AstréeA prototype is a fork of the Astrée static analyzer that adds support for analyzing parallel embedded C software.
  • URL:
  • Contact:
    Patrick Cousot
  • Participants:
    Antoine Miné, Jerome Feret, Patrick Cousot, Radhia Cousot, Xavier Rival
  • Partners:
    CNRS, ENS Paris, AbsInt Angewandte Informatik GmbH

7.1.4 ClangML

  • Keyword:
  • Functional Description:
    ClangML is an OCaml binding with the Clang front-end of the LLVM compiler suite. Its goal is to provide an easy to use solution to parse a wide range of C programs, that can be called from static analysis tools implemented in OCaml, which allows to test them on existing programs written in C (or in other idioms derived from C) without having to redesign a front-end from scratch. ClangML features an interface to a large set of internal AST nodes of Clang , with an easy to use API. Currently, ClangML supports all C language AST nodes, as well as a large part of the C nodes related to C++ and Objective-C.
  • URL:
  • Contact:
    Xavier Rival
  • Participants:
    Devin Mccoughlin, François Berenger, Pippijn Van Steenhoven

7.1.5 FuncTion

  • Scientific Description:
    FuncTion is based on an extension to liveness properties of the framework to analyze termination by abstract interpretation proposed by Patrick Cousot and Radhia Cousot. FuncTion infers ranking functions using piecewise-defined abstract domains. Several domains are available to partition the ranking function, including intervals, octagons, and polyhedra. Two domains are also available to represent the value of ranking functions: a domain of affine ranking functions, and a domain of ordinal-valued ranking functions (which allows handling programs with unbounded non-determinism).
  • Functional Description:
    FuncTion is a research prototype static analyzer to analyze the termination and functional liveness properties of programs. It accepts programs in a small non-deterministic imperative language. It is also parameterized by a property: either termination, or a recurrence or a guarantee property (according to the classification by Manna and Pnueli of program properties). It then performs a backward static analysis that automatically infers sufficient conditions at the beginning of the program so that all executions satisfying the conditions also satisfy the property.
  • URL:
  • Contact:
    Caterina Urban
  • Participants:
    Antoine Miné, Caterina Urban

7.1.6 HOO

  • Name:
    Heap Abstraction for Open Objects
  • Functional Description:

    JSAna with HOO is a static analyzer for JavaScript programs. The primary component, HOO, which is designed to be reusable by itself, is an abstract domain for a dynamic language heap. A dynamic language heap consists of open, extensible objects linked together by pointers. Uniquely, HOO abstracts these extensible objects, where attribute/field names of objects may be unknown. Additionally, it contains features to keeping precise track of attribute name/value relationships as well as calling unknown functions through desynchronized separation.

    As a library, HOO is useful for any dynamic language static analysis. It is designed to allow abstractions for values to be easily swapped out for different abstractions, allowing it to be used for a wide-range of dynamic languages outside of JavaScript.

  • Contact:
    Arlen Cox
  • Participant:
    Arlen Cox

7.1.7 MemCAD

  • Name:
    The MemCAD static analyzer
  • Keywords:
    Static analysis, Abstraction
  • Functional Description:
    MemCAD is a static analyzer that focuses on memory abstraction. It takes as input C programs, and computes invariants on the data structures manipulated by the programs. It can also verify memory safety. It comprises several memory abstract domains, including a flat representation, and two graph abstractions with summaries based on inductive definitions of data-structures, such as lists and trees and several combination operators for memory abstract domains (hierarchical abstraction, reduced product). The purpose of this construction is to offer a great flexibility in the memory abstraction, so as to either make very efficient static analyses of relatively simple programs, or still quite efficient static analyses of very involved pieces of code. The implementation consists of over 30 000 lines of ML code, and relies on the ClangML front-end. The current implementation comes with over 300 small size test cases that are used as regression tests.
  • URL:
  • Contact:
    Xavier Rival
  • Participants:
    Antoine Toubhans, François Berenger, Huisong Li, Xavier Rival

7.1.8 KAPPA

  • Name:
    A rule-based language for modeling interaction networks
  • Keywords:
    Systems Biology, Modeling, Static analysis, Simulation, Model reduction
  • Scientific Description:
    OpenKappa is a collection of tools to build, debug and run models of biological pathways. It contains a compiler for the Kappa Language, a static analyzer (for debugging models), a simulator, a compression tool for causal traces, and a model reduction tool.
  • Functional Description:
    Kappa is provided with the following tools: - a compiler - a stochastic simulator - a static analyzer - a trace compression algorithm - an ODE generator.
  • Release Contributions:
    On line UI, Simulation is based on a new data-structure (see ESOP 2017 ), New abstract domains are available in the static analyzer (see SASB 2016), Local traces (see TCBB 2018), Reasoning on polymers (see SASB 2018).
  • URL:
  • Contact:
    Jerome Feret
  • Participants:
    Jean Krivine, Jerome Feret, Kim-Quyen Ly, Pierre Boutillier, Russ Harmer, Vincent Danos, Walter Fontana, Antoine Pouille, Matthieu Bougueon
  • Partners:
    ENS Lyon, Université Paris-Diderot, HARVARD Medical School

7.1.9 QUICr

  • Functional Description:
    QUICr is an OCaml library that implements a parametric abstract domain for sets. It is constructed as a functor that accepts any numeric abstract domain that can be adapted to the interface and produces an abstract domain for sets of numbers combined with numbers. It is relational, flexible, and tunable. It serves as a basis for future exploration of set abstraction.
  • Contact:
    Arlen Cox
  • Participant:
    Arlen Cox

7.1.10 Zarith

  • Functional Description:

    Zarith is a small (10K lines) OCaml library that implements arithmetic and logical operations over arbitrary-precision integers. It is based on the GNU MP library to efficiently implement arithmetic over big integers. Special care has been taken to ensure the efficiency of the library also for small integers: small integers are represented as Caml unboxed integers and use a specific C code path. Moreover, optimized assembly versions of small integer operations are provided for a few common architectures.

    Zarith is currently used in the Astrée analyzer to enable the sound analysis of programs featuring 64-bit (or larger) integers. It is also used in the Frama-C analyzer platform developed at CEA LIST and Inria Saclay.

  • URL:
  • Contact:
    Antoine Miné
  • Participants:
    Antoine Miné, Pascal Cuoq, Xavier Leroy

7.1.11 PYPPAI

  • Name:
    Pyro Probabilistic Program Analyzer
  • Keywords:
    Probability, Static analysis, Program verification, Abstraction
  • Functional Description:

    PYPPAI is a program analyzer to verify the correct semantic definition of probabilistic programs written in Pyro. At the moment, PYPPAI verifies consistency conditions between models and guides used in probabilistic inference programs.

    PYPPAI is written in OCaml and uses the pyml Python in OCaml library. It features a numerical abstract domain based on Apron, an abstract domain to represent zones in tensors, and dedicated abstract domains to describe distributions and states in probabilistic programs.

  • URL:
  • Contact:
    Xavier Rival

8 New results

8.1 Foundations

A Categorical Framework for Program Semantics and Semantic Abstraction.

Participants: Jérémy Dubut, Shin-ya Katsumata, Xavier Rival [correspondant].

Categorical semantics of type theories are often characterized as structure-preserving functors. This is because in category theory both the syntax and the domain of interpretation are uniformly treated as structured categories, so that we can express interpretations as structure-preserving functors between them. This mathematical characterization of semantics makes it convenient to manipulate and to reason about relationships between interpretations. Motivated by this success of functorial semantics, we address the question of finding a functorial analogue in abstract interpretation, a general framework for comparing semantics, so that we can bring similar benefits of functorial semantics to semantic abstractions used in abstract interpretation. Major differences concern the notion of interpretation that is being considered. Indeed, conventional semantics are value-based whereas abstract interpretation typically deals with more complex properties. In this paper, we propose a functorial approach to abstract interpretation and study associated fundamental concepts therein. In our approach, interpretations are expressed as oplax functors in the category of posets, and abstraction relations between interpretations are expressed as lax natural transformations representing concretizations. We present examples of these formal concepts from monadic semantics of programming languages and discuss soundness.

This work has been accepted for publishation at MFPS 2023 17.

8.2 Abstract domains


A generic framework to coarse-grain stochastic reaction networks by Abstract Interpretation

Participants: Jérôme Boillot, Jérôme Feret.

In 12, we present symbolic methods to improve the precision of static analyses of modular integer expressions based on Abstract Interpretation. Like similar symbolic methods, the idea is to simplify on-the-fly arithmetic expressions before they are given to abstract transfer functions of underlying abstract domains. When manipulating fixed-length integer data types, casts and overflows generally act like modulo computations which hinder the use of symbolic techniques. The goal of this article is to formalize how modulo operations can be safely eliminated by abstracting arbitrary arithmetic expressions into sum, product, or division of linear forms with integer coefficients, while simplifying them. We provide some rules to simplify arithmetic expressions that are involved in the computation of linear interpolations, while ensuring the soundness of the transformation.

All these methods have been incorparated in three static analyzers: a toy analyzer publicly available, the ASTRÉE statis analyzer, and the MOPSA open-source static analysis platform. In particular, MOPSA aims at broadening their application to the general software development community. The symbolic simplification of expressions involving modular integer expressions turned out to be very useful to solve some corner cases that other tools could not attack. Jérôme Boillot has participated to the team Mopsa who won the Gold Medal (Winner) of SV-Comp's SoftwareSystems category 2024. The competition will take place at TACAS 2024. The detailed results are available at: https://sv-comp.sosy-lab.org/2024/results/results-verified/.

A Formal Framework to Measure the Incompleteness of Abstract Interpretations

Participants: Marco Campion, Caterina Urban, Mila Dalla Preda, Roberto Giacobazzi.

In program analysis by abstract interpretation, backward-completeness represents no loss of precision between the result of the analysis and the abstraction of the concrete execution, while forward-completeness stands for no imprecision between the concretization of the analysis result and the concrete execution. Program analyzers satisfying one of the two properties (or both) are considered precise. Regrettably, as for all approximation methods, the presence of false alarms is most of the time unavoidable and therefore we need to deal somehow with incompleteness of both. To this end, a new property called partial completeness has recently been formalized as a relaxation of backward-completeness allowing a limited amount of imprecision measured by quasi-metrics. However, the use of quasi-metrics enforces distance functions to adhere precisely the abstract domain ordering, thus not suitable to be used to weaken the forward-completeness property which considers also abstract domains that are not necessarily based on Galois Connections. In 13 (published at SAS 2023), we formalize a weaker form of quasi-metric, called pre-metric, which can be defined on all domains equipped with a pre-order relation. We show how this newly defined notion of pre-metric allows us to derive other pre-metrics on other domains by exploiting the concretization and, when available, the abstraction maps, according to the information and the corresponding level of approximation that we want to measure. Finally, by exploiting pre-metrics as our imprecision meter, we introduce the partial forward/backward-completeness properties.

Monotonicity and the Precision of Program Analysis

Participants: Marco Campion, Mila Dalla Preda, Roberto Giacobazzi, Caterina Urban.

It is widely known that the precision of a program analyzer is closely related to intensional program properties, namely, properties concerning how the program is written. Less is known about a possible relation between what the program extensionally computes, namely, its input-output relation, and the precision of a program analyzer. In our paper 4 accepted for publication at POPL 2024, we explore this potential connection in an effort to isolate program fragments that can be precisely analyzed by abstract interpretation, namely, programs for which there exists a complete abstract interpretation. In the field of static inference of numeric invariants, this happens for programs, or parts of programs, that manifest a monotone (either non-decreasing or non-increasing) behavior. In the paper, we first formalize the notion of program monotonicity with respect to a given input and a set of numerical variables of interest. A sound proof system is then introduced with judgments specifying whether a program is monotone relatively to a set of variables and a set of inputs. The interest in monotonicity is justified because we prove that the family of monotone programs admits a complete abstract interpretation over a specific class of non-trivial numerical abstractions and inputs. This class includes all non-relational abstract domains that refine interval analysis (i.e., at least as precise as the intervals abstraction) and that satisfy a topological convexity hypothesis.

8.3 Causal analysis

Participants: Jérôme Feret [correspondant], Aurélie Kong Win Chang, Grégor Goeßler.

In 18, we introduce a small step semantics for a subset of Core Erlang modeling its monitoring and signal systems. The goal of our semantics is to enable the construction of causal explanations for property violations, which will be the object of future work. As a first axis of reflection, we chose to study the impact of the order of messages on a faulty behavior. We present our semantics and discuss some of our design choices. This work is a part of a broader project on causal debugging of concurrent programs in Erlang.

8.4 Application to computational systems biology

Software sciences have a role to play in the description, the organization, the execution, and the analysis of the molecular interaction systems such as biological signaling pathways. These systems involve a huge diversity of bio-molecular entities whereas their dynamics may be driven by races for shared resources, interactions at different time- and concentration-scales, and non-linear feedback loops. Understanding how the behavior of the populations of proteins orchestrates itself from their individual interactions, which is the holy grail on systems biology, requires dedicated languages offering adapted levels of abstraction and efficient analysis tools.

Static analysis and model reduction

Participants: Jérôme Feret.

In our habilitation thesis 24, we describe the design of formal tools for Kappa, a site-graph rewriting language inspired by bio-chemistry. In particular, we introduce a static analysis to compute some properties on the biological entities that may arise in models, so as to increase our confidence in them. We also present a model reduction approach based on a study of the flow of information between the different regions of the biological entities and the potential symmetries. This approach is applied both in the differential and in the stochastic semantics.

The first three chapters of 24 forms the material for a course that has been taught at EJCIM 2023, the PhD spring school of the CNRS research group informatic mathematics (GDR IM) 27.

Faithful Model Reduction of Discrete Biological Systems

Participants: Jérôme Feret, Albin Salazar.

In the last decades, logical or discrete models have emerged as a successful paradigm for capturing and predicting the behaviors of systems of molecular interactions. Intuitively, they consist in sampling the abundance of each kind of biochemical entity within finite sets of intervals and deriving transitions accordingly. On one hand, formallyproven sound derivation from more precise descriptions (such as from reaction networks) may include many fictitious behaviors. On the other hand, direct modeling usually favors dominant interactions with no guarantee on the behaviors that are neglected.

In his PhD 28 from which is also extracted the paper 15, Albin Salazar formalize a sound coarse-graining approach for stochastic reaction networks. Its originality relies on two main ingredients. Firstly, we abstract values by intervals that overlap in order to introduce a minimal effort for the system to go back to the previous interval, hence limiting fictitious oscillations in the coarse-grained models. Secondly, we compute for pairs of transitions (in the coarse-grained model) bounds on the probabilities on which one will occur first. We illustrate our ideas on two case studies and demonstrate how techniques from Abstract Interpretation can be used to design more precise discretization methods, while providing a framework to further investigate the underlying structure of logical and discrete models.

Modeling populations of hepatic stellar cells

Participants: Matthieu Bouguéon, Jérôme Feret, Anne Siegel, Nathalie Théret.

Hepatic fibrosis is an excessive response to cicatrisation that is induced by chronical lesions. It is characterised by an accumulation of the extracellular matrix, mainly made of collagene, which increases the rigidity of tissues and leads to severe liver disorders. The activation of hepatic stellar cells, induced by the TGF-β growth factor is the main processus at the origin of hepatic fibrosis.

So as to study the dynamics of hepatic stellar cells during the development and the reversion of bibrosis, Matthieu Bouguéon has, in his PhD thesis 26, codirectied by Anne Siegel and Nathalie Théret, and comentored by Jérôme Feret, developped a multi-scale model integrating several states of the hepatic stellar cells and their production of collagene, under the influence of TGF-β1. This model is implemented in Kappa. Besides being the first multi-scale model in Kappa, this model captures the plasticity of stellar cells during the development and the reversion of fibrosis. The model predicts that the inactivation of fibrosis plays an essential role in the development of fibrosis. The model has been validated by new experiments in mouses and the predictions have been validated by RNAseq data in fibrotic patients.

8.5 Static Analysis of Machine Learning Software

Verifying Attention Robustness of Deep Neural Networks against Semantic Perturbations

Participants: Satoshi Munakata, Caterina Urban, Haruki Yokoyama, Koji Yamamoto, Kazuki Munakata.

  It is known that deep neural networks (DNNs) classify an input image by paying particular attention to certain specific pixels; a graphical representation of the magnitude of attention to each pixel is called a saliency-map. Saliency-maps are used to check the validity of the classification decision basis, e.g., it is not a valid basis for classification if a DNN pays more attention to the background rather than the subject of an image. Semantic perturbations can significantly change the saliency-map. In 20, we propose the first verification method for attention robustness, i.e., the local robustness of the changes in the saliency-map against combinations of semantic perturbations. Specifically, our method determines the range of the perturbation parameters (e.g., the brightness change) that maintains the difference between the actual saliency-map change and the expected saliency-map change below a given threshold value. Our method is based on activation region traversals, focusing on the outermost robust boundary for scalability on larger DNNs. Experimental results demonstrate that our method can show the extent to which DNNs can classify with the same basis regardless of semantic perturbations and report on performance and performance factors of activation region traversals.

Abstract Interpretation-Based Feature Importance for Support Vector Machines

Participants: Abhinandan Pal, Francesco Ranzato, Caterina Urban, Marco Zanella.

In 22 (accepted for publication at VMCAI 2024), we propose a symbolic representation for support vector machines (SVMs) by means of abstract interpretation, a well-known and successful technique for designing and implementing static program analyses. We leverage this abstraction in two ways: (1) to enhance the interpretability of SVMs by deriving a novel feature importance measure, called abstract feature importance (AFI), that does not depend in any way on a given dataset of the accuracy of the SVM and is very fast to compute, and (2) for verifying stability, notably individual fairness, of SVMs and producing concrete counterexamples when the verification fails. We implemented our approach and we empirically demonstrated its effectiveness on SVMs based on linear and nonlinear (polynomial and radial basis function) kernels. Our experimental results show that, independently of the accuracy of the SVM, our AFI measure correlates much more strongly with the stability of the SVM to feature perturbations than feature importance measures widely available in machine learning software such as permutation feature importance. It thus gives better insight into the trustworthiness of SVMs.

8.6 Static Analysis of Jupyter Notebooks

Static Analysis of Data Transformations in Jupyter Notebooks

Participants: Luca Negrini, Guruprerana Shabadi, Caterina Urban.

Jupyter notebooks used to pre-process and polish raw data for data science and machine learning processes are challenging to analyze. Their data-centric code manipulates dataframes through call to library functions with complex semantics, and the properties to track over it vary widely depending on the verification task. In 21 (published at SOAP 2023), we presents a novel abstract domain that simplifies writing analyses for such programs, by extracting a unique Control Flow Graph (CFG) from the notebook that contains all transformations applied to the data. Several properties can then be determined by analyzing such CFG, that is simpler than the original Python code. In the paper, we present a first use case that exploits our analysis to infer the required shape of the dataframes manipulated by the notebook.

8.7 Shape analysis

A Product of Shape and Sequence Abstractions.

Participants: Josselin Giet, Félix Ridoux, Xavier Rival [correspondant].

Traditional separation logic-based shape analyses utilize in- ductive summarizing predicates so as to capture general properties of the layout of data-structures, to verify accurate manipulations of, e.g., various forms of lists or trees. However, they also usually abstract away contents properties, so that they may only verify memory safety and invariance of data-structure shapes. In this paper, we introduce a novel abstract domain to describe sequences of values of unbounded size, and track constraints on their length and on extremal values contained in them. We define a reduced product of such a sequence abstraction together with an existing shape abstraction so as to infer both shape and contents properties of data-structures. We report on the implementation of the sequence domain, its integration into a static analyzer for C code, and we evaluate its ability to verify partial functional correctness properties for list and tree algorithms.

This work has been accepted for publishation at SAS 2023 16.

8.8 Static Analysis of Probabilistic Programming Languages and Optimization Algorithms

Towards the verification of semantic assumptions required by probabilistic inference algorithms

Participants: Wonyeol Lee, Hangyeol Wu, Xavier Rival [correspondant], Hongseok Yang.

Probabilistic programming is the idea of writing models from statistics and machine learning using program notations and reasoning about these models using generic inference engines. Recently its combination with deep learning has been explored intensely, which led to the development of so called deep probabilistic programming languages, such as Pyro, Edward and ProbTorch. At the core of this development lie inference engines based on stochastic variational inference algorithms. When asked to find information about the posterior distribution of a model written in such a language, these algorithms convert this posterior-inference query into an optimisation problem and solve it approximately by a form of gradient ascent or descent. We analysed one of the most fundamental and versatile variational inference algorithms, called score estimator or REINFORCE, using tools from denotational semantics and program analysis. We formally expressed what this algorithm does on models denoted by programs, and exposed implicit assumptions made by the algorithm on the models. The violation of these assumptions may lead to an undefined optimisation objective or the loss of convergence guarantee of the optimisation process. We then describe rules for proving these assumptions, which can be automated by static program analyses. Some of our rules use nontrivial facts from continuous mathematics, and let us replace requirements about integrals in the assumptions, such as integrability of functions defined in terms of programs’ denotations, by conditions involving differentiation or boundedness, which are much easier to prove automatically (and manually). Following our general methodology, we have developed a static program analysis for the Pyro programming language that aims at discharging the assumption about what we call model-guide support match. Our analysis is applied to the eight representative model-guide pairs from the Pyro webpage, which include sophisticated neural network models such as AIR. It found a bug in one of these cases, and revealed a non-standard use of an inference engine in another, and showed that the assumptions are met in the remaining six cases.

Moreover, we have implemented an analysis for differentiability and other classes of smoothness properties. This analysis can be ran on regular Python programs or on Pyro programs, and verify the differentiability properties required for the sound definition of model guide pairs.,

The basis for this method has been published at POPL 2020 37.

Smoothness Analysis for Probabilistic Programs with Application to Optimised Variational Inference

Participants: Wonyeol Lee, Xavier Rival [correspondant], Hongseok Yang.

We proposed a static analysis for discovering differentiable or more generally smooth parts of a given probabilistic program, and showed how the analysis can be used to improve the pathwise gradient estimator, one of the most popular methods for posterior inference and model learning. Our improvement increases the scope of the estimator from differentiable models to non-differentiable ones without requiring manual intervention of the user; the improved estimator automatically identifies differentiable parts of a given probabilistic program using our static analysis, and applies the pathwise gradient estimator to the identified parts while using a more general but less efficient estimator, called score estimator, for the rest of the program. Our analysis has a surprisingly subtle soundness argument, partly due to the misbehaviours of some target smoothness properties when viewed from the perspective of program analysis designers. For instance, some smoothness properties, such as partial differentiability and partial continuity, are not preserved by function composition, and this makes it difficult to analyse sequential composition soundly without heavily sacrificing precision. We formulated five assumptions on a target smoothness property, prove the soundness of our analysis under those assumptions, and show that our leading examples satisfy these assumptions. We have also shown that by using information from our analysis instantiated for differentiability, our improved gradient estimator satisfies an important differentiability requirement and thus computes the correct estimate on average (i.e., returns an unbiased estimate) under a regularity condition. Our experiments with representative probabilistic programs in the Pyro language show that our static analysis is capable of identifying smooth parts of those programs accurately, and making our improved pathwise gradient estimator exploit all the opportunities for high performance in those programs.

This work has been accepted for publication at POPL 2023 10.

8.9 Static analysis for security properties

Sound Symbolic Execution via Abstract Interpretation and its Application to Security

Participants: Tamara Rezk, Xavier Rival [correspondant], Ignacio Tiraboschi.

Symbolic execution is a program analysis technique commonly utilized to determine whether programs violate properties and, in case violations are found, to generate inputs that can trigger them. Used in the context of security properties such as noninterference, symbolic execution is precise when looking for counter-example pairs of traces when insecure information flows are found, however it is sound only up to a bound thus it does not allow to prove the correctness of programs with executions beyond the given bound. By contrast, abstract interpretation-based static analysis guarantees soundness but generally lacks the ability to provide counter-example pairs of traces.

In this work, we propose to weave both to obtain the best of two worlds. We demonstrate this with a series of static analyses, including a static analysis called DSym aimed at verifying noninterference. DSym provides both semantically sound results and the ability to derive counter-example pairs of traces up to a bound. It relies on a combination of symbolic execution and abstract domains inspired by the well known notion of reduced product. We formalize DSym and prove its soundness as well as its relative precision up to a bound. We also provide a prototype implementation of DSym and evaluate it on a sample of challenging examples.

This work has been accepted for publication at VMCAI 2023 23.

8.10 Reductions between synchronous and asynchronous programming abstractions


Testing consensus implementations using communication closure

Participants: Cezara Drăgoi, Constantin Enea, Burcu Kulahcioglu Ozkan, Rupak Majumdar, Filip Niksic.


Large scale production distributed systems are difficult to design and test. Correctness must be ensured when processes run asynchronously, at arbitrary rates relative to each other, and in the presence of failures, e.g., process crashes or message losses. These conditions create a huge space of executions that is difficult to explore in a principled way. Current testing techniques focus on systematic or randomized exploration of all executions of an implementation while treating the implemented algorithms as black boxes. On the other hand, proofs of correctness of many of the underlying algorithms often exploit semantic properties that reduce reasoning about correctness to a subset of behaviors. For example, the communication-closure property, used in many proofs of distributed consensus algorithms, shows that every asynchronous execution of the algorithm is equivalent to a lossy synchronous execution, thus reducing the burden of proof to only that subset. In a lossy synchronous execution, processes execute in lock-step rounds, and messages are either received in the same round or lost forever—such executions form a small subset of all asynchronous ones.

In 36 we formulate the communication-closure hypothesis, which states that bugs in implementations of distributed consensus algorithms will already manifest in lossy synchronous executions and present a testing algorithm based on this hypothesis. We prioritize the search space based on a bound on the number of failures in the execution and the rate at which these failures are recovered. We show that a random testing algorithm based on sampling lossy synchronous executions can empirically find a number of bugs—including previously unknown ones—in production distributed systems such as Zookeeper, Cassandra, and Ratis, and also produce more understandable bug traces.

8.11 Distributed algorithms

Geometric bounds for convergence rates of averaging algorithms

Participants: Bernadette Charron-Bost.

  We developed a generic method for bounding the convergence rate of an averaging algorithm running in a multi-agent system with a time-varying network, where the associated stochastic matrices have a time-independent Perron vector. This method provides bounds on convergence rates that unify and refine most of the previously known bounds. They depend on geometric parameters of the dynamic communication graph such as the normalized diameter or the bottleneck measure. As corollaries of these geometric bounds, we show that the convergence rate of the Metropolis algorithm in a system of n agents is less than 1-0.25n2 with any communication graph that may vary in time, but is permanently connected and bidirectional. We prove a similar upper bound for the EqualNeighbor algorithm under the additional assumptions that the number of neighbors of each agent is constant and that the communication graph is not too irregular. Moreover our bounds offer improved convergence rates for several averaging algorithms and specific families of communication graphs. Finally we extend our methodology to a time-varying Perron vector and show how convergence times may dramatically degrade with even limited variations of Perron vectors.

Computing Outside the Box: Average Consensus over Dynamic Networks

Participants: Bernadette Charron-Bost, Patrick Lambein-Monette.

  Networked systems of autonomous agents, and applications thereof, often rely on the control primitive of average consensus, where the agents are to compute the average of private initial values. To provide reliable services that are easy to deploy, average consensus should continue to operate when the network is subject to frequent and unpredictable change, and should mobilize few computational resources, so that deterministic, low powered, and anonymous agents can partake in the network. In this stringent adversarial context, we investigated the implementation of average consensus by distributed algorithms over networks with bidirectional, but potentially short-lived, communication links. Inspired by convex recurrence rules for multi-agent systems, and the Metropolis average consensus rule in particular, we designed a deterministic distributed algorithm that achieves asymptotic average consensus, which we show to operate in polynomial time in a synchronous temporal model. The algorithm is easy to implement, has low space and computational complexity, and is fully distributed, requiring neither symmetry-breaking devices like unique identifiers, nor global control or knowledge of the network. In the fully decentralized model that we adopt, to our knowledge, no other distributed average consensus algorithm has a better temporal complexity. Our approach distinguishes itself from classical convex recurrence rules in that the agent’s values may sometimes leave their previous convex hull. As a consequence, our convergence bound requires a subtle analysis, despite the syntactic simplicity of our algorithm.

8.12 Modeling

A Kappa model for hepatic stellate cells activation by TGFB1

Participants: Matthieu Bougéon, Pierre Boutillier, Jérôme Feret, Octave Hazard, Nathalie Théret.

We model as a realistic case study, a population of hepatic stellate cells under the effect of the TGFB1 protein. In this case study, the components will be occurrences of hepatic stellate cells in different states, and occurrences of the protein TGFB1. The protein TGFB1 induces different behaviors of hepatic stellate cells thereby contributing either to tissue repair or to fibrosis. Better understanding the overall behavior of the mechanisms that are involved in these processes is a key issue to identify markers and therapeutic targets likely to promote the resolution of fibrosis at the expense of its progression.

8.13 Static analysis of signaling pathways

Static analysis for rule-based models

Participants: Jérôme Feret.

In the context biochemical systems, in the first steps of modeling, static analysis helps the modeler by warning about potential issues in the model. Then it provides useful properties to check that what is implemented is what the modeler has in mind and to provide a quick overview of the model for the people who have not written it. We recall the basic ingredients of the language Kappa and we explain how local patterns can be used as a cornerstone to build extensible static analyses.

Rate Equations for Graphs

Participants: Vincent Danos, Tobias Heindel, Ricardo Honorato-Zimmer, Sandro Stucki.

We combine ideas from: 1) graph transformation systems (GTSs) stemming from the theory of formal languages and concurrency, and 2) mean field approximations (MFAs), a collection of approximation techniques ubiquitous in the study of complex dynamics to build a framework which generates rate equations for stochastic GTSs and from which one can derive MFAs of any order (no longer limited to the humanly computable). The procedure for deriving rate equations and their approximations can be automated. An implementation and example models are available online. We apply our techniques and tools to derive an expression for the mean velocity of a two-legged walker protein on DNA.

9 Bilateral contracts and grants with industry

9.1 Bilateral contracts with industry

9.1.1 Disco project with Tezos

Participants: Bernadette Charron-Bost, Cezara Drăgoi, Jérôme Feret, Xavier Rival.

  • Title: DISCO: Synchronous Abstractions for Blockchain Infrastructures
  • Type: Research contracts funded by Tezos
  • Duration: September 2020 - September 2023
  • Inria contact: Xavier Rival, Jérôme Feret
  • Abstract: The literature in distributed computing distinguishes two main classes of computational models: asynchronous models have better performance, whereas synchronous models provide stronger formal guarantees. Implementations of distributed systems must operate in asynchronous models of computation, where performance emerges from the load of the system. The correctness of asynchronous protocols is very hard to prove, due to the challenges of concurrency, faults, buffered message queues, and message loss, altering, and re-ordering by the network. In contrast, synchronous models are based on (communication- closed) rounds, and this structure greatly facilitates verification. There are no interleavings, and the cumulative size of reception buffers is bounded by the number of processes in the network.

    The goal of this project is to increase the confidence we have in blockchain systems. We propose to: (1) define a synchronous computational model for blockchain algorithms and build a domain-specific language appropriate for this synchronous computational model, (2) equip the domain-specific language with support for mechanized formal verification with a high degree of automation, and (3) prototypically implement a dedicated runtime for efficiently executing, within an asynchronous context, algorithms defined for a synchronous models, together with a formal correctness proof that certifies the correctness of the synchronous abstraction with respect to the asynchronous runtime.

10 Partnerships and cooperations

10.1 International initiatives

10.1.1 Associate Teams in the framework of an Inria International Lab or in the framework of an Inria International Program

  • AISAPPL (Abstract Interpretation-based Static Analysis of Probabilistic Programming Languages), 2023–2025

    Xavier Rival (INRIA Antique), Hongseok Yang (KAIST, South Korea)

    The purpose of this associated team is to formalize conditions ensuring the well-definedness of the semantics of probabilistic programs, and to investigate the application of static analysis techniques in order to guarantee these conditions hold. It mainly targets the Pyro probabilistic programming language (an overlay of Python, initially developped at Uber AI), but it studies concepts that are of general interest in probabilistic programming.

10.2 International research visitors

10.2.1 Visits of international scientists

Other international visits to the team

As part of the AISAPPL INRIA Associate INRIA Team, Hongseok Yang visited ANTIQUE during Summer 2023 for one week.

10.2.2 Visits to international teams

Research stays abroad

Xavier Rival was invited for a one week visit at the University of Edinburgh for collaboration with Ohad Kammar.

Xavier Rival visited KAIST as part of the AISAPPL INRIA Associate Team.

Xavier Rival was Invited Professor at SNU (Seoul National University) for 5 weeks in Fall 2023.

10.3 National initiatives

10.3.1 DCore

Participants: Jérôme Feret, Gregor Gössler, Jean Krivine, Ivan Lanese, Claudio Antares Mezzina, Davide Sangiorgi, Jean-Bernard Stefani, German Vidál, Gianluigi Zavattaro.

  • Title: DCore - Causal Debugging for Concurrent Systems
  • Type: ANR générique 2018
  • Defi: Société de l'information et de la communication
  • Instrument: ANR grant
  • Duration: March 2019 - February 2023
  • Coordinator: INRIA Grenoble - Rhône-Alpes (France)
  • Others partners: IRIF (France), Inria Paris (France)
  • Inria contact: Jérôme Feret
  • Abstract: As software takes over more and more functionalities in embedded and safety-critical systems, bugs may endanger the safety of human beings and of the environment, or entail heavy financial losses. In spite of the development of verification and testing techniques, debugging still plays a crucial part in the arsenal of the software developer. Unfortunately, usual debugging techniques do not scale to large concurrent and distributed systems: they fail to provide precise and efficient means to inspect and analyze large concurrent executions; they do not provide means to automatically reveal software faults that constitute actual causes for errors; and they do not provide succinct and relevant explanations linking causes (software bugs) to their effects (errors observed during execution).

    The overall objective of the project is to develop a semantically well-founded, novel form of concurrent debugging, which we call "causal debugging”, that aims to alleviate the deficiencies of current debugging techniques for large concurrent software systems.

    Briefly, the causal debugging technology developed by the DCore project will comprise and integrate two main novel engines:

    1. A reversible execution engine that allows programmers to backtrack and replay a concurrent or distributed program execution, in a way that is both precise and efficient (only the exact threads involved by a return to a target anterior or posterior program state are impacted);
    2. a causal analysis engine that allows programmers to analyze concurrent executions, by asking questions of the form "what caused the violation of this program property?”, and that allows for the precise and efficient investigation of past and potential program executions.

    The project will build its causal debugging technology on results obtained by members of the team, as part of the past ANR project REVER, on the causal semantics of concurrent languages, and the semantics of concurrent reversible languages, as well as on recent works by members of the project on abstract interpretation, causal explanations and counterfactual causal analysis.

    The project primarily targets multithreaded, multicore and multiprocessor software systems, and functional software errors, that is errors that arise in concurrent executions because of faults (bugs) in software that prevents it to meet its intended function. Distributed systems, which can be impacted by network failures and remote site failures are not an immediate target for DCore, although the technology developed by the project should constitute an important contribution towards full-fledged distributed debugging. Likewise, we do not target performance or security errors, which come with specific issues and require different levels of instrumentation, although the DCore technology should prove a key contribution in these areas as well.

10.3.2 SAFTA

  • Title: SAFTA Static Analysis for Fault-Tolerant distributed Algorithms.
  • Type: ANR JCJC 2018
  • Duration: February 2018 - August 2023
  • Coordinator: Cezara Drăgoi, CR Inria
  • Abstract: Fault-tolerant distributed data structures are at the core distributed systems. Due to the multiple sources of non-determinism, their development is challenging. The project aims to increase the confidence we have in distributed implementations of data structures. We think that the difficulty does not only come from the algorithms but from the way we think about distributed systems. In this project we investigate partially synchronous communication-closed round based programming abstractions that reduce the number of interleavings, simplifying the reasoning about distributed systems and their proof arguments. We use partial synchrony to define reduction theorems from asynchronous semantics to partially synchronous ones, enabling the transfer of proofs from the synchronous world to the asynchronous one. Moreover, we define a domain specific language, that allows the programmer to focus on the algorithm task, it compiles into efficient asynchronous code, and it is equipped with automated verification engines.

10.3.3 ANR VeriAMOS

  • Title: Verification of Abstract Machines for Operating Systems
  • Type: ANR générique 2018
  • Defi: Société de l'information et de la communication
  • Instrument: ANR grant
  • Duration: January 2019 - July 2024
  • Coordinator: INRIA Paris (France)
  • Others partners: LIP6 (France), IRISA (France), UGA (France)
  • Inria contact: Xavier Rival
  • Abstract: Operating System (OS) programming is notoriously difficult and error prone. Moreover, OS bugs can have a serious impact on the functioning of computer systems. Yet, the verification of OSes is still mostly an open problem, and has only been done using user-assisted approaches that require a huge amount of human intervention. The VeriAMOS proposal relies on a novel approach to automatically and fully verifying OS services, that combines Domain Specific Languages (DSLs) and automatic static analysis. In this approach, DSLs provide language abstraction and let users express complex policies in high-level simple code. This code is later compiled into low level C code, to be executed on an abstract machine. Last, the automatic static analysis verifies structural and robustness properties on the abstract machine and generated code. We will apply this approach to the automatic, full verification of input/output schedulers for modern supports like SSDs.

10.3.4 ANR EMASS

  • Title: Analyse Mémoire Efficace de Logiciel Système
  • Type: ANR appel 2022
  • Defi: CE39 - Sécurité globale, résilience et gestion de crise, cybersécurité
  • Instrument: ANR grant
  • Duration: 2023 - 2027
  • Coordinator: CEA Saclay
  • Others partners: INRIA (France), Thalés (France)
  • Inria contact: Xavier Rival
  • Abstract: The goal of this project is to develop and integrate static analysis techniques that target memory properties for low level code (such as operating system code), in order both to establish safety and security properties. As part of this project, antique is carrying out research on the analysis of programs using complex data-structures.

10.3.5 PEPR SecurEval

  • Title: SecurEval, Improving Digital Systems Security Evaluation
  • Type: PEPR
  • Defi: PEPR Cybersécurité
  • Instrument: PEPR
  • Duration: 2022 - 2028
  • Coordinator: CEA Saclay
  • partners: CNRS, INRIA, CEA, INP Grenoble, Supelec, UGA, Université Paris Saclay, Université Sorbonne nouvelle
  • Inria contact: Xavier Rival and Jérôme Feret
  • Abstract: This project targets methods to improve the security of software, using programming languages techniques (static analysis, testing, programming languages). It gathers a large number of academic partners (CNRS, INRIA, CEA, INP Grenoble, Supelec, UGA, Université Paris Saclay, Université Sorbonne nouvelle). As part of this project, antique is investigating static analysis techniques for the verification of safety and security proeprties.

10.3.6 PEPR SAIF

  • Title: PEPR SAIF
  • Type: PEPR
  • Defi: PEPR IA
  • Instrument: PEPR
  • Duration: 2022 - 2028
  • Coordinator: CEA Saclay
  • partners: INRIA Paris (project team antique), INRIA Saclay (project team TAU), and INRIA Rennes (project team SuMo), Université Paris-Saclay (Formal Methods Laboratory, LMF), École Polytechnique (Computer Science Laboratory, LIX), CEA-List (Software Safety &Security Lab, LSL), and Université de Bordeaux (Bordeaux Computer Science Laboratory)
  • Inria contact: Caterina Urban
  • Abstract: SAIF is a project led by Caterina Urban within the PEPR IA. The consortium includes INRIA Paris (project team antique), INRIA Saclay (project team TAU), and INRIA Rennes (project team SuMo), as well as Université Paris-Saclay (Formal Methods Laboratory, LMF), École Polytechnique (Computer Science Laboratory, LIX), CEA-List (Software Safety &Security Lab, LSL), and Université de Bordeaux (Bordeaux Computer Science Laboratory).

    The overall goal of SAIF is to use the vast knowledge accumulated over decades in formal methods to rethink them and address the novel safety concerns raised by machine learning-based systems.

10.3.7 INRIA Challenge SPAI

(Security Program Analyses for IoT), 2019–2023

Coordinated by Tamara Rezk (INDES), and with Daniel Le Métayer (PRIVATICS) Xavier Rival (ANTIQUE) Manuel Serrano (INDES) Alan Schmitt (EPICURE) Robert de Simone (KAIROS)

This project aims at developing programming languages techniques to reason over security properties of Internet of Things devices, where several clients, servers, and devices may communicate, and where devices may either act upon or observe the physical world, hereby contributing to information flows. The project already led to the design of not only a programming language able to describe such systems but also of verification techniques for security.

11 Dissemination

11.1 Promoting scientific activities

11.1.1 Scientific events: organisation

General chair, scientific chair
  • Caterina Urban is a member of the Steering Committee of the International Static Analysis Symposium (SAS).
  • Caterina Urban is a member of the Steering Committee of the International Workshop on the State Of the Art in Program Analysis (SOAP).
  • Caterina Urban is a member of the Steering Committee of the series of Summer Schools on Foundations of Programming and Software Systems (FoPSS).
  • Caterina Urban is a member of the ETAPS Executive Board.
Member of the organizing committees
  • Caterina Urban is a member of the organizing committee of the Mentoring Workshop at ETAPS 2024.
  • Jérôme Feret, Xavier Rival, and Caterina Urban are members of the organizing committee of the N40AI Workshop at POPL 2024.
  • Caterina Urban was a member of the organizing committee of the Mentoring Workshop at ETAPS 2023.

11.1.2 Scientific events: selection

Chair of conference program committees
  • Caterina Urban is chairing the committee of the ETAPS Doctoral Dissertation Award 2024.
  • Caterina Urban chaired the committee of the ETAPS Doctoral Dissertation Award 2023.
Member of the conference program committees
  • Jérôme Feret served as a Member of the Program Committee of VMCAI 2023 (Verification, Model Checking, and Abstract Interpretation).
  • Caterina Urban is serving as a Member of the Program Committee of FoSSaCS 2025 (Foundations of Software Science and Computation Structure).
  • Caterina Urban is serving as a Member of the Program Committee of LPAR 2024 (Logic for Programming, Artificial Intelligence and Reasoning).
  • Caterina Urban is serving as a Member of the Program Committee of CAV 2024 (Computer-Aided Verification).
  • Caterina Urban is serving as a Member of the Program Committee of TACAS 2024 (Tools and Algorithms for the Construction and Analysis of Systems).
  • Caterina Urban served as a Member of the Program Committee of CAV 2023 (Computer-Aided Verification).
  • Caterina Urban served as a Member of the Program Committee of NFM 2024 (NASA Formal Methods).
  • Caterina Urban served as a Member of the Program Committee of ESOP 2023 (European Symposium On Programming).
  • Xavier Rival served as a Member of the Programm Committee of VMCAII 2024 (Verification, Model Checking and Abstract Interpretation)
  • Xavier Rival is serving as a Member of the Programm Committee of PLDI 2024 (Symposium on Programming Languages and Implementation)
  • Xavier Rival is serving as a Member of the Programm Committee of CSF 2024 (Conference on Security Foundations)
  • Xavier Rival is serving as a Member of the Programm Committee of SAS 2024 (Static Analysis Symposium)
  • Jérôme Feret served as a Reviewer for POPL 2023 (Principle of Programming Languages 2023).

11.1.3 Journal

Member of the editorial boards
  • Caterina Urban is serving as Associated Editor for Transactions on Programming Languages and Systems (TOPLAS).
  • Caterina Urban is serving as a Guest Editor for the Special Issue on SAS 2022 of Formal Methods in System Design (FMSD).
  • Caterina Urban is serving as a Guest Editor for the Special Issue on CAV 2020 of Formal Methods in System Design (FMSD).
Reviewer - reviewing activities
  • Jérôme Feret served as a reviewer for CNSNS (Communications in Nonlinear Science and Numerical Simulation), TCBB (Transactions on Computational Biology and Bioinformatics), TCS (Theoretical Computer Sciences).

11.1.4 Invited talks

  • Caterina Urban will give an invited talk at the 17th International Scientific Conference on Informatics (Informatics 2024).
  • Caterina Urban will give an invited talk at the 29th Journées Formalisation des Activités Concurrentes (FAC 2024).
  • Caterina Urban will give an invited talk at Quarkslab, Paris.
  • Caterina Urban gave an invited talk at the International Symposium on Model Checking of Software (SPIN 2023).
  • Caterina Urban gave an invited talk at CEA-List, Palaiseau.
  • Caterina Urban gave an invited talk at the Séminaire IRILL of the Center for Research and Innovation on Free Software.
  • Xavier Rival gaven an invited talk at the Seminar of the University of Edinburgh.

11.1.5 Leadership within the scientific community

Xavier Rival is a member of the IFIP Working Group 2.4 on Software Implementation Technologies.

11.1.6 Scientific expertise

  • Caterina Urban is a member of the Scientific Advisory Board of the Laboratoire Méthodes Formelles (LMF) de l’Université Paris-Saclay.
  • Caterina Urban served as a member of the Assessment Committee for Associate Professor in Systems and Software Engineering at the University of Copenhagen.

11.1.7 Research administration

  • Jérôme Feret is a Member of the Laboratory Council of the Department of Computer Science of École normale supérieure.
  • Jérôme Feret is a Member of the PhD Review Committee (CSD) of Inria Paris.
  • Jérôme Feret is Dean of Study of the Department of Computer Science of École normale supérieure.
  • Xavier Rival is a Member of the Laboratory Council of the Department of Computer Science of École normale supérieure.
  • Xavier Rival is a Member of the Evaluation Committee of INRIA.


11.2 Teaching - Supervision - Juries

11.2.1 Teaching

  • Licence:
    • Jérôme Feret and Xavier Rival (lectures), and Josselin Giet (tutorials), “Semantics and Application to Verification”, 36h, L3, at École Normale Supérieure, France.
  • Master:
    • Bernadette Charron-Bost, ”Calculability in multi-agent networks”, 24h, M2, Parisian Master of Research in Computer Science (MPRI), France.
    • Bernadette Charron-Bost, ”Consensus problems”, 24h, M1 Ecole Polytechnique Master
    • Jérôme Feret, Antoine Miné, Xavier Rival, and Caterina Urban, “Abstract Interpretation: application to verification and static analysis”, 72h, M2. Parisian Master of Research in Computer Science (MPRI), France.
    • Jérôme Feret and François Fages, “Biochemical Programming”, 24h, M2. Parisian Master of Research in Computer Science (MPRI), France.
    • Jérôme Feret, Jean Krivine, Sébastien Légaré, and Matthieu Bouguéon. "Rule-based Modelling", 24h, M1. Interdisciplinary Approaches to Life Science (AIV), Master Program, Université Paris-Descartes, France.
    • Xavier Rival gave a lecture on Formal Methods for Systems Security at the EXED.
  • PhD::
    • Jérôme Feret, "Analyse statique et réduction de modèles de voies de signalisation intracellulaire", 6h, PhD School of the CNRS Informatics (EJCIM 2023) - Mathematics research group (GDR IM), Poitier, France.

11.2.2 Supervision

  • Internship: Bernadette Charron-Bost and Jérôme Feret surpervised the research project of Sylvain Gay (4rd year student at ENS) and Vincent Peth (2nd year student at ENS). Fibration in graphs and application to modular proofs of distributed algorithms.
  • Internship: Caterina Urban supervised the M2 ENS Rennes internship of Naïm Moussaoui-Remil, from March 2023 to August 2023, on “Static Analyses for Robust (Un)reachability”.
  • Internship: Caterina Urban supervised the Master internship of Kevin Pinochet (University of Chile), from January 2023 to April 2024, on “Input Data Usage Analyses for Jupyter Notebooks”.
  • Internship: Caterina Urban supervised the Bachelor internship of Abhinandan Pal (IIT Kalyani), from November 2022 to January 2023, on “Attention Robustness Static Analysis”.
  • Internship: Xavier Rival supervised the Master Internship of Charles De Haro from March 2023 till August 2023 on the static analysis based inference for smoothness properties (Paris MPRI Master)
  • PhD in progress: Jérôme Boillot, Static Analysis of the setting of expanded memory in a dedicated operating system, started in 2022 and supervised by Jérôme Feret.
  • PhD in progress: Aurélie Kong Win Chang, Abstractions for causal analysis and explanations in concurrent programs, started in 2021 and supervised by Gregor Gössler (INRIA Grenoble - Rhône Alpes, Project team Spades) and Jérôme Feret.
  • PhD in progress: Naïm Moussaoui-Remil, Static Analyses for Robust (Un)reachability, started in 2023 and supervised by
  • Phd in progress: Serge Durand, Formal Specification of Machine Learning Algorithms, started in 2021 and supervised by Zakaria Chihani (CEA/List) and Caterina Urban.
  • Phd in progress: Denis Mazzucato, Static Analysis by Abstract Interpretation of Quantitative Extensional Program Properties, started in 2020 and supervised by Caterina Urban.
  • PhD in progress: Valentin Barbazo, Static analysis of parallel programs operating over unbounded dynamic data-structures, started in 2023, and supervised by Xavier Rival.
  • PhD in progress: Josselin Giet, Static Analysis of components of operating systems by abstract interpretation, started in 2020 and supervised by Xavier Rival.
  • PhD in progress: Ignacio Tiraboschi, Static analysis of security properties for IoT systems, started in 2020 and co-supervised by Tamara Rezk (EP Indes) and Xavier Rival.
  • PhD defended: Albin Salazar, Formal derivation of discrete models with separated time-scales, started in 2019 and supervised by Jérôme Feret.
  • PhD defended: Matthieu Bouguéon, Modélisation de la dynamique des cellules étoilées hépatiques durant le developpement et la réversion de la fibrose, started in 2020 and supervised by Nathalie Théret and Anne Siegel, and mentored by Jérôme Feret.

11.2.3 Juries

  • Bernadette Charron-Bost served as a jury member for the Habilitation Thesis Committee of Jérôme Feret (ENS).
  • Jérôme Feret served as a member of the Review Committee for the PhD of Giann Karlo Aguirre Samboni at École normale supérieure of Paris-Saclay (Defense: December 2023).
  • Caterina Urban will serve as a Jury member for the defense of the PhD of Olivier Martinot (Université Paris Cité, Defense: May or June 2023).
  • Xavier Rival served as reviewer and president for the Habilitation Thesis Committee of Arthur Charguéraud (University of Strasbourg).
  • Xavier Rival served as a reviewer and jury member for the PhD of Santiago-Sara Bautista (Université of Rennes I).
  • Xavier Rival served as a jury member for the Habilitation Thesis Committee of Jérôme Feret (ENS).

11.3 Popularization

11.3.1 Internal or external Inria responsibilities

  • Jérôme Feret served in the “admissibility” jury for INRIA researcher positions (CRCN) for the center of “Paris” in 2023.
  • Jérôme Feret served in the “admissibility” jury for INRIA researcher positions (CRCN) for the center of “Paris-Saclay” in 2023.
  • Jérôme Feret is a Member of the PhD Review Committee (CSD) of Inria Paris.
  • Jérôme Feret is head of study of the department of computer science of École normale supérieure.
  • Jérôme Feret is member of the laboratory board of the department of computer sciences of École normale supérieure.

11.3.2 Interventions

  • Jérôme Feret hosted eight fourteen years old students during three hours within the Antique team.

12 Scientific production

12.1 Major publications

  • 1 inproceedingsJ.Julien Bertrane, P.Patrick Cousot, R.Radhia Cousot, J.Jérôme Feret, L.Laurent Mauborgne, A.Antoine Miné and X.Xavier Rival. Static Analysis and Verification of Aerospace Software by Abstract Interpretation.Proceedings of the American Institute of Aeronautics and Astronautics (AIAA Infotech@Aerospace 2010)Atlanta, Georgia, USAAmerican Institute of Aeronautics and Astronautics2010
  • 2 inproceedingsB.Bruno Blanchet, P.Patrick Cousot, R.Radhia Cousot, J.Jérôme Feret, L.Laurent Mauborgne, A.Antoine Miné, D.David Monniaux and X.Xavier Rival. A Static Analyzer for Large Safety-Critical Software.Proceedings of the ACM SIGPLAN 2003 Conference on Programming Language Design and Implementation (PLDI'03)ACM PressJune 7--14 2003, 196--207HAL
  • 3 inproceedingsA.Ahmed Bouajjani, C.Cezara Dragoi, C.Constantin Enea and M.Mihaela Sighireanu. On inter-procedural analysis of programs with lists and data.Proceedings of the 32nd ACM SIGPLAN Conference on Programming Language Design and Implementation, PLDI 2011, San Jose, CA, USA, June 4-8, 20112011, 578--589URL: http://doi.acm.org/10.1145/1993498.1993566DOI
  • 4 articleM.Marco Campion, M.Mila Dalla Preda, R.Roberto Giacobazzi and C.Caterina Urban. Monotonicity and the Precision of Program Analysis.Proceedings of the ACM on Programming Languages8POPLJanuary 2024, 1629-1662HALDOIback to text
  • 5 articleP.Patrick Cousot. Constructive Design of a Hierarchy of Semantics of a Transition System by Abstract Interpretation.Theoretical Computer Science2771--22002, 47--103
  • 6 articleJ.Jérôme Feret, V.Vincent Danos, J.Jean Krivine, R.Russ Harmer and W.Walter Fontana. Internal coarse-graining of molecular systems.Proceeding of the national academy of sciences10616Apr 2009
  • 7 inproceedingsL.Laurent Mauborgne and X.Xavier Rival. Trace Partitioning in Abstract Interpretation Based Static Analyzers.Proceedings of the 14th European Symposium on Programming (ESOP'05)3444Lecture Notes in Computer ScienceSpringer-Verlag2005, 5--20
  • 8 articleA.Antoine Miné. The Octagon Abstract Domain.Higher-Order and Symbolic Computation192006, 31--100
  • 9 inproceedingsX.Xavier Rival. Symbolic Transfer Functions-based Approaches to Certified Compilation.Conference Record of the 31st Annual ACM SIGPLAN~-- SIGACT Symposium on Principles of Programming LanguagesACM Press, New York, United States2004, 1--13

12.2 Publications of the year

International journals

International peer-reviewed conferences

  • 12 inproceedingsJ.Jérôme Boillot and J.Jérôme Feret. Symbolic transformation of expressions in modular arithmetic.Static Analysis: 30th International Symposium, SAS 2023Static Analysis: 30th International Symposium, SAS 2023Static Analysis: 30th International Symposium, SAS 2023Cascais, PortugalOctober 2023HALback to text
  • 13 inproceedingsM.Marco Campion, C.Caterina Urban, M. D.Mila Dalla Preda and R.Roberto Giacobazzi. A Formal Framework to Measure the Incompleteness of Abstract Interpretations.30th International Static Analysis Symposium (SAS 2023)30th International Static Analysis Symposium (SAS 2023)30th International Static Analysis Symposium (SAS 2023)Cascais, PortugalOctober 2023HALback to text
  • 14 inproceedingsB.Bernadette Charron-Bost and L.Louis Penet de Monterno. Self-Stabilizing Clock Synchronization in Probabilistic Networks.DISC 2023 - 37th International Symposium on Distributed Computing281L'Aquila, Italie, ItalySchloss Dagstuhl - Leibniz-Zentrum für Informatik2023, 12:1--12:18HALDOI
  • 15 inproceedingsJ.Jérôme Feret and A.Albin Salazar. A generic framework to coarse-grain stochastic reaction networks by Abstract Interpretation.VMCAI 2023 - 24th International Conference on Verification, Model Checking and Abstract InterpretationBoston, United StatesJanuary 2023HALback to text
  • 16 inproceedingsJ.Josselin Giet, F.Félix Ridoux and X.Xavier Rival. A Product of Shape and Sequence Abstractions.Static AnalysisStatic Analysis: 30th International Symposium, SAS 2023Static Analysis: 30th International Symposium, SAS 2023Cascais, PortugalOctober 2023HALback to text
  • 17 inproceedingsS.-Y.Shin-Ya Katsumata, X.Xavier Rival and J.Jérémy Dubut. A Categorical Framework for Program Semantics and Semantic Abstraction.MFPS 2023 - Mathematical Foundations of Program SemanticsBloomington, United StatesSeptember 2023HALback to text
  • 18 inproceedingsA.Aurélie Kong Win Chang, J.Jerome Feret and G.Gregor Gössler. A Semantics of Core Erlang with Handling of Signals.ACM Digital LibraryErlang 2023 - 22nd ACM SIGPLAN International Workshop on ErlangSeattle WA, United StatesACM2023, 31-38HALDOIback to text
  • 19 inproceedingsB.Baptiste Lepers, J.Josselin Giet, J.Julia Lawall and W.Willy Zwaenepoel. OFence: Pairing Barriers to Find Concurrency Bugs in the Linux Kernel.EuroSys 2023 : Eighteenth European Conference on Computer SystemsRome, ItalyACMMay 2023, 33-45HALDOI
  • 20 inproceedingsS.Satoshi Munakata, C.Caterina Urban, H.Haruki Yokoyama, K.Koji Yamamoto and K.Kazuki Munakata. Verifying Attention Robustness of Deep Neural Networks Against Semantic Perturbations.15th International Symposium on NASA Formal Methods (NFM 2023)13903Lecture Notes in Computer ScienceHouston (TX), United StatesSpringer Nature SwitzerlandJune 2023, 37-61HALDOIback to text
  • 21 inproceedingsL.Luca Negrini, G.Guruprerana Shabadi and C.Caterina Urban. Static Analysis of Data Transformations in Jupyter Notebooks.12th ACM SIGPLAN International Workshop on the State Of the Art in Program Analysis (SOAP 2023)12th ACM SIGPLAN International Workshop on the State Of the Art in Program Analysis (SOAP 2023)Orlando FL, United StatesACMJune 2023, 8-13HALDOIback to text
  • 22 inproceedingsA.Abhinandan Pal, F.Francesco Ranzato, C.Caterina Urban and M.Marco Zanella. Abstract Interpretation-Based Feature Importance for Support Vector Machines.25th International Conference on Verification, Model Checking, and Abstract Interpretation (VMCAI 2024)14499Lecture Notes in Computer ScienceLondon, United KingdomSpringer Nature SwitzerlandDecember 2024, 27-49HALDOIback to text
  • 23 inproceedingsI.Ignacio Tiraboschi, T.Tamara Rezk and X.Xavier Rival. Sound Symbolic Execution via Abstract Interpretation and its Application to Security.Lecture Notes in Computer ScienceVMCAI 2023 - 24th International Conference on Verification, Model Checking, and Abstract Interpretation13881Verification, Model Checking, and Abstract Interpretation 24th International Conference, VMCAI 2023, Boston, MA, USA, January 16–17, 2023, ProceedingBoston, MA, United StatesSpringer Nature SwitzerlandJanuary 2023, 267-295HALDOIback to text

Scientific book chapters

  • 24 inbookJ.Jérôme Feret. Analyse statique et réduction de modèles de voies de signalisation intracellulaire.Informatique Mathématique Une photographie en 2023CNRSJune 2023, 67HALback to textback to text
  • 25 inbookC.Caterina Urban. Static Analysis for Data Scientists.238Challenges of Software VerificationIntelligent Systems Reference LibrarySpringer Nature SingaporeJuly 2023, 77-91HALDOI

Doctoral dissertations and habilitation theses

  • 26 thesisM.Matthieu Bouguéon. Kappa modeling of hepatic stellate cell dynamics during fibrosis development and reversion.Université de Rennes (2023-....)December 2023HALback to text
  • 27 thesisJ.Jérôme Feret. Analyse statique et réduction de modèles pour un langage de réécriture de graphes à sites.ENS-PSLDecember 2023HALback to text
  • 28 thesisA.Albin Salazar. Faithful model reduction of discrete biological systems.ENS ParisNovember 2023HALback to text

Reports & preprints

12.3 Cited publications

  • 34 articleP.Patrick Cousot. Constructive design of a hierarchy of semantics of a transition system by abstract interpretation.Electr. Notes Theor. Comput. Sci.61997, 77--102URL: http://dx.doi.org/10.1016/S1571-0661(05)80168-9DOIback to text
  • 35 inproceedingsP.Patrick Cousot and R.Radhia Cousot. Abstract interpretation: a unified lattice model for static analysis of programs by construction or approximation of fixpoints.Conference Record of the Fourth Annual ACM SIGPLAN-SIGACT Symposium on Principles of Programming LanguagesACM Press, New York, United States1977, 238--252back to textback to text
  • 36 inproceedingsC.Cezara Dragoi, C.Constantin Enea, B. K.Burcu Kulahcioglu Ozkan, R.Rupak Majumdar and F.Filip Niksic. Testing consensus implementations using communication closure.SPLASH 2020 : ACM SIGPLAN conference on Systems, Programming, Languages, and Applications: Software for HumanityChiccago / Virtual, United StatesOctober 2021HALDOIback to text
  • 37 articleW.Wonyeol Lee, H.Hangyeol Yu, X.Xavier Rival and H.Hongseok Yang. Towards Verified Stochastic Variational Inference for Probabilistic Programs.Proceedings of the ACM on Programming Languages162020HALDOIback to text
  • 38 inproceedingsC.Caterina Urban. Static Analysis of Data Science Software.SAS 2019 - 26th Static Analysis SymposiumPorto, PortugalSpringer10 2019, 17-23HALDOIback to text