Hycomes was created a local team of the Rennes - Bretagne Atlantique Inria research center in 2013 and has been created as an Inria Project-Team in 2016. The team is focused on two topics in cyber-physical systems design:

Systems industries today make extensive use of mathematical modeling tools to design computer controlled physical systems. This class of tools addresses the modeling of physical systems with models that are simpler than usual scientific computing problems by using only Ordinary Differential Equations (ODE) and Difference Equations but not Partial Differential Equations (PDE). This family of tools first emerged in the 1980's with SystemBuild by MatrixX (now distributed by National Instruments) followed soon by Simulink by Mathworks, with an impressive subsequent development.

In the early 90's control scientists from the University of Lund (Sweden) realized that the above approach did not support component based modeling of physical systems with reuse 1. For instance, it was not easy to draw an electrical or hydraulic circuit by assembling component models of the various devices. The development of the Omola language by Hilding Elmqvist was a first attempt to bridge this gap by supporting some form of Differential Algebraic Equations (DAE) in the models. Modelica quickly emerged from this first attempt and became in the 2000's a major international concerted effort with the Modelica Consortium 2. A wider set of tools, both industrial and academic, now exists in this segment 3. In the EDA sector, VHDL-AMS was developed as a standard 52 and also allows for differential algebraic equations. Several domain-specific languages and tools for mechanical systems or electronic circuits also support some restricted classes of differential algebraic equations. Spice is the historic and most striking instance of these domain-specific languages/tools 4. The main difference is that equations are hidden and the fixed structure of the differential algebraic results from the physical domain covered by these languages.

Despite these tools are now widely used by a number of engineers, they raise a number of technical difficulties. The meaning of some programs, their mathematical semantics, is indeed ambiguous. A main source of difficulty is the correct simulation of continuous-time dynamics, interacting with discrete-time dynamics: How the propagation of mode switchings should be handled? How to avoid artifacts due to the use of a global ODE solver causing unwanted coupling between seemingly non interacting subsystems? Also, the mixed use of an equational style for the continuous dynamics with an imperative style for the mode changes and resets is a source of difficulty when handling parallel composition. It is therefore not uncommon that tools return complex warnings for programs with many different suggested hints for fixing them. Yet, these “pathological” programs can still be executed, if wanted so, giving surprising results — See for instance the Simulink examples in 24, 20 and 21.

Indeed this area suffers from the same difficulties that led to the development of the theory of synchronous languages as an effort to fix obscure compilation schemes for discrete time equation based languages in the 1980's. Our vision is that hybrid systems modeling tools deserve similar efforts in theory as synchronous languages did for the programming of embedded systems.

Non-Standard analysis plays a central role in our research on hybrid systems modeling 20, 24, 22, 21. The following text provides a brief summary of this theory and gives some hints on its usefulness in the context of hybrid systems modeling. This presentation is based on our paper 2, a chapter of Simon Bliudze's PhD thesis 30, and a recent presentation of non-standard analysis, not axiomatic in style, due to the mathematician Lindström 58.

Non-standard numbers allowed us to reconsider the semantics of hybrid
systems and propose a radical alternative to the super-dense
time semantics developed by Edward Lee and his team as part of the
Ptolemy II project, where cascades of successive instants can occur in
zero time by using infinitesimal and non-standard
integers. Remark that (1) non-standard semantics
provides a framework that is familiar to the computer
scientist and at the same time efficient as a symbolic
abstraction. This makes it an excellent candidate for the development
of provably correct compilation schemes and type systems for hybrid
systems modeling languages.

Non-standard analysis was proposed by Abraham Robinson in the 1960s to allow the explicit manipulation of “infinitesimals” in analysis 67, 45, 41. Robinson's approach is axiomatic; he proposes adding three new axioms to the basic Zermelo-Fraenkel (ZFC) framework. There has been much debate in the mathematical community as to whether it is worth considering non-standard analysis instead of staying with the traditional one. We do not enter this debate. The important thing for us is that non-standard analysis allows the use of the non-standard discretization of continuous dynamics “as if” it was operational.

Not surprisingly, such an idea is quite ancient. Iwasaki et al. 53 first proposed using non-standard analysis to discuss the nature of time in hybrid systems. Bliudze and Krob 29, 30 have also used non-standard analysis as a mathematical support for defining a system theory for hybrid systems. They discuss in detail the notion of “system” and investigate computability issues. The formalization they propose closely follows that of Turing machines, with a memory tape and a control mechanism.

The Modelica language is based on Differential Algebraic Equations (DAE). The general form of a DAE is given by:

where

Let leading variables of

The state variables of

A leading variable algebraic
if

DAE are a strict generalization of ordinary differential
equations (ODE), in the sense that it may not be immediate
to rewrite a DAE as an explicit ODE of the form

For a square DAE of dimension

can locally be made explicit, i.e., the Jacobian matrix of differentiation
index 35 of

In practice, the problem of automatically finding a ”minimal”
solution structural nonsingularity of the Jacobian matrix, i.e., its
almost certain nonsingularity when its nonzero entries vary over some
neighborhood. In this framework, the structural analysis
(SA) of a DAE returns, when successful, values of the

A renowned method for the SA of DAE is the Pantelides method;
however, Pryce's $\Sigma $-method is introduced also in what
follows, as it is a crucial tool for our works.

In 1988, Pantelides proposed what is probably the most well-known SA method for DAE 64. The leading idea of his work is that the structural representation of a DAE can be condensed into a bipartite graph whose left nodes (resp. right nodes) represent the equations (resp. the variables), and in which an edge exists if and only if the variable occurs in the equation.

By detecting specific subsets of the nodes, called Minimally
Structurally Singular (MSS) subsets, the Pantelides method
iteratively differentiates part of the equations until a perfect
matching between the equations and the leading variables is found. One
can easily prove that this is a necessary and sufficient condition for
the structural nonsingularity of the system.

The main reason why the Pantelides method is not used in our work is that it cannot efficiently be adapted to multimode DAE (mDAE). As a matter of fact, the adjacency graph of a mDAE has both its nodes and edges parametrized by the subset of modes in which they are active; this, in turn, requires that a parametrized Pantelides method must branch every time no mode-independent MSS is found, ultimately resulting, in the worst case, in the enumeration of modes.

Albeit less renowned that the Pantelides method, Pryce's
$\Sigma $-matrix, or

This matrix is given by:

where

The primal problem consists in finding a maximum-weight
perfect matching (MWPM) in the weighted adjacency
graph. This is actually an assignment problem, for the solving of
which several standard algorithms exist, such as the push-relabel
algorithm 51 or the Edmonds-Karp
algorithm 47 to only give a few. However, none of
these algorithms are easily parametrizable, even for applications to
mDAE systems with a fixed number of variables.

The dual problem consists in finding the component-wise minimal
solution fixpoint
iteration (FPI) that makes use of the MWPM found as a
solution to the primal problem, described by the set of tuples

From the results proved by Pryce in 65, it is known
that the above algorithm terminates if and only if it is provided a
MWPM, and that the values it returns are independent of the choice of
a MWPM whenever there exist several such matchings. In particular, a
direct corollary is that the

Another important result is that, if the Pantelides method succeeds
for a given DAE

Working with this method is natural for our works, since the algorithm for solving the dual problem is easily parametrizable for dealing with multimode systems, as shown in our recent paper 34.

Once structural analysis has been performed, system

System companies such as automotive and aeronautic companies are facing significant difficulties due to the exponentially raising complexity of their products coupled with increasingly tight demands on functionality, correctness, and time-to-market. The cost of being late to market or of imperfections in the products is staggering as witnessed by the recent recalls and delivery delays that many major car and airplane manufacturers had to bear in the recent years. The specific root causes of these design problems are complex and relate to a number of issues ranging from design processes and relationships with different departments of the same company and with suppliers, to incomplete requirement specification and testing.

We believe the most promising means to address the challenges in systems engineering is to employ structured and formal design methodologies that seamlessly and coherently combine the various viewpoints of the design space (behavior, space, time, energy, reliability, ...), that provide the appropriate abstractions to manage the inherent complexity, and that can provide correct-by-construction implementations. The following technology issues must be addressed when developing new approaches to the design of complex systems:

The challenge is to address the entire process and not to consider only local solutions of methodology, tools, and models that ease part of the design.

Contract-based design has been proposed as a new approach to
the system design problem that is rigorous and effective in dealing
with the problems and challenges described before, and that, at the
same time, does not require a radical change in the way industrial
designers carry out their task as it cuts across design flows of
different types.
Indeed, contracts can be used almost everywhere and at nearly all
stages of system design, from early requirements capture, to embedded
computing infrastructure and detailed design involving circuits and
other hardware. Contracts explicitly handle pairs of properties,
respectively representing the assumptions on the environment and the
guarantees of the system under these assumptions. Intuitively, a
contract is a pair

A detailed bibliography on contract and interface theories for embedded system design can be found in 3. In a nutshell, contract and interface theories fall into two main categories:

Requirements Engineering is one of the major concerns in large systems industries today, particularly so in sectors where certification prevails 68. Most requirements engineering tools offer a poor structuring of the requirements and cannot be considered as formal modeling frameworks today. They are nothing less, but nothing more than an informal structured documentation enriched with hyperlinks. As examples, medium size sub-systems may have a few thousands requirements and the Rafale fighter aircraft has above 250,000 of them. For the Boeing 787, requirements were not stable while subcontractors were working on the development of the fly-by-wire and of the landing gear subsystems, leading to a long and cahotic convergence of the design process.

We see Contract-Based Design and Interfaces Theories as innovative tools in support of Requirements Engineering. The Software Engineering community has extensively covered several aspects of Requirements Engineering, in particular:

Behavioral models and properties, however, are not properly encompassed by the above approaches. This is the cause of a remaining gap between this phase of systems design and later phases where formal model based methods involving behavior have become prevalent—see the success of Matlab/Simulink/Scade technologies. We believe that our work on contract based design and interface theories is best suited to bridge this gap.

The Hycomes team contributes to the design of mathematical modeling languages and tools, to be used for the design of cyberphysical systems. In a nutshell, two major applications can be clearly identified: (i) our work on the structural analysis of multimode DAE systems has a sizeable impact on the techniques to be used in Modelica tools; (ii) our work on the verification of dynamical systems has an impact on the design methodology for safety-critical cyberphysical systems. These two applications are detailed below.

Mathematical modeling tools are a considerable business, with major actors such as MathWorks, with Matlab/Simulink, or Wolfram, with Mathematica. However, none of these prominent tools are suitable for the engineering of large systems. The Modelica language has been designed with this objective in mind, making the best of the advantages of DAEs to support a component-based approach. Several industries in the energy sector have adopted Modelica as their main systems engineering language.

Although multimode features have been introduced in version 3.3 of the language 48, proper tool support of multimode models is still lagging behind. The reason is not a lack of interest from tool vendors and academia, but rather that multimode DAE systems poses several fundamental difficulties, such as a proper definition of a concept of solutions for multimode DAEs, how to handle mode switchings that trigger a change of system structure, or how impulsive variables should be handled. Our work on multimode DAEs focuses on these crucial issues 6.

Thanks to the experimental coupling of Dymola (Dassault Systèmes'
commercial implementation of the Modelica language) with our IsamDAE
prototype (https://

In addition to well-defined operational semantics for hybrid systems, one often needs to provide formal guarantees about the behavior of some critical components of the system, or at least its main underlying logic. To do so, we are actively developing new techniques to automatically verify whether a hybrid system complies with its specifications, and/or to infer automatically the envelope within which the system behaves safely. The approaches we developed have been already successfully used to formally verify the intricate logic of the ACAS X, a mid-air collision avoidance system that advises the pilot to go upward or downward to avoid a nearby airplane which requires mixing the continuous motion of the aircraft with the discrete decisions to resolve the potential conflict 54. This challenging example is nothing but an instance of the kind of systems we are targeting: autonomous smart systems that are designed to perform sophisticated tasks with an internal tricky logic. What is even more interesting perhaps is that such techniques can be often "reverted" to actually synthesize missing components so that some property holds, effectively helping the design of such complex systems.

The expected impact of our research is to allow both better designs and better exploitation of energy production units and distribution networks, enabling large-scale energy savings. At least, this is what we can observe in the context of the FUI ModeliScale collaborative project, which is focused on electric grids, urban heat networks and building thermal modeling.

The rationale is as follows: system engineering models are meant to assess the correctness, safety and optimality of a system under design. However, system models are still useful after the system has been put in operation. This is especially true in the energy sector, where systems have an extremely long lifespan (for instance, more than 50 years for some nuclear power plants) and are upgraded periodically, to integrate new technologies. Exactly like in software engineering, where a software and its model co-evolve throughout the lifespan of the software, a co-evolution of the system and its physical models has to be maintained. This is required in order to maintan the safety of the system, but also its optimality.

Moreover, physical models can be instrumental to the optimal exploitation of a system. A typical example are model-predictive control (MPC) techniques, where the model is simulated, during the exploitation of the system, in order to predict system trajectories up to a bounded-time horizon. Optimal control inputs can then be computed by mathematical programming methods, possibly using multiple simulation results. This has been proved to be a practical solution 50, whenever classical optimal control methods are ineffective, for instance, when the system is non-linear or discontinuous. However, this requires the generation of high-performance simulation code, capable of simulating a system much faster than real-time.

The structural analysis techniques implemented in IsamDAE 8 generate a conditional block dependency graph, that can be used to generate high-performance simulation code : static code can be generated for each block of equations, and a scheduling of these blocks can be computed, at runtime, at each mode switching, thanks to an inexpensive topological sort algorithm. Contrarily to other approaches (such as 49), no structural analysis, block-trangular decompositions, or automatic differentiation has to be performed at runtime.

The main highlights for 2020 are the two following achievements:

Demodocos is used to construct a Test and Flip net (Petri net variant) from a collection of instances of a given procedure. The tool takes as input either standard XES log files (a standard XML file format for process mining tools) or a specific XML file format for surgical applications. The result is a Test and Flip net and its marking graph. The tool can also build a #SEVEN scenario for integration into a virtual reality environment. The scenario obtained corresponds to the generalization of the input instances, namely the instances synthesis enriched with new behaviors respecting the relations of causality, conflicts and competition observed.

Demodocos is a synthesis tool implementing a linear algebraic polynomial time algorithm. Computations are done in the Z/2Z ring. Test and Flip nets extend Elementary Net Systems by allowing test to zero, test to one and flip arcs. The effect of flip arcs is to complement the marking of the place. While the net synthesis problem has been proved to be NP hard for Elementary Net Systems, thanks to flip arcs, the synthesis of Test and Flip nets can be done in polynomial time. Test and flip nets have the required expressivity to give concise and accurate representations of surgical processes (models of types of surgical operations). Test and Flip nets can express causality and conflict relations. The tool takes as input either standard XES log files (a standard XML file format for process mining tools) or a specific XML file format for surgical applications. The output is a Test and Flip net, solution of the following synthesis problem: Given a finite input language (log file), compute a net, which language is the least language in the class of Test and Flip net languages, containing the input language.

The tool Demodocos allows to build a generic model for a given procedure from some examples of instances of this procedure. The generated model can take the form of a graph, a Test 'n Flip net or a SEVEN scenario (intended for integration into a virtual reality environment).

The classic use of the tool is to apply the summary operation to a set of files describing instances of the target procedure. Several file formats are supported, including the standard XES format for log events. As output, several files are generated. These files represent the generic procedure in different forms, responding to varied uses.

This application is of limited interest in the case of an isolated use, out of context and without a specific objective when using the model generated. It was developed as part of a research project focusing in particular on surgical procedures, and requiring the generation of a generic model for integration into a virtual reality training environment. It is also quite possible to apply the same method in another context.

Modeling languages and tools based on Differential Algebraic Equations (DAE) bring several specific issues that do not exist with modeling languages based on Ordinary Differential Equations. The main problem is the determination of the differentiation index and latent equations. Prior to generating simulation code and calling solvers, the compilation of a model requires a structural analysis step, which reduces the differentiation index to a level acceptable by numerical solvers.

The Modelica language, among others, allows hybrid models with multiple modes, mode-dependent dynamics and state-dependent mode switching. These Multimode DAE (mDAE) systems are much harder to deal with. The main difficulties are (i) the combinatorial explosion of the number of modes, and (ii) the correct handling of mode switchings.

The aim of the software is on the first issue, namely: How can one perform a structural analysis of an mDAE in all possible modes, without enumerating these modes? A structural analysis algorithm for mDAE systems has been designed and implemented, based on an implicit representation of the varying structure of an mDAE. It generalizes J. Pryce's Sigma-method to the multimode case and uses Binary Decision Diagrams (BDD) to represent the mode-dependent structure of an mDAE. The algorithm determines, as a function of the mode, the set of latent equations, the leading variables and the state vector. This is then used to compute a mode-dependent block-triangular decomposition of the system, that can be used to generate simulation code with a mode-dependent scheduling of the blocks of equations.

IsamDAE (Implicit Structural Analysis of Multimode DAE systems) is a software library implementing new structural analysis algorithms for multimode DAE systems, based on an implicit representation of incidence graphs, matchings between equations and variables, and block decompositions. The input of the software is a variable dimension multimode DAE system consisting in a set of guarded equations and guarded variable declarations. It computes a mode-dependent structural index reduction of the multimode system and produces a mode-dependent graph for the scheduling of blocks of equations. It also computes the differentiation order of the latent equations and leading variables, as functions of the modes.

IsamDAE is coded in OCaml, and uses (at least partially) the following packages: * MLBDD by Arlen Cox, * Menhir by François Pottier and Yann Régis-Gianas, * GuaCaml and Snowflake by Joan Thibault, * Pprint by François Pottier, * XML-Light by Nicolas Cannasse and Jacques Garrigue.

Versions 0.3a to 0.3d (released between Mar. and Dec. 2020):

* Performance improvements: connection with the Snowflake package by Joan Thibault, based on his PhD works on RBTF (Reduced Block-Triangular Forms). The order in which variables and equations are declared in the model, and the way these declarations are grouped, has way less impact on performances when RBTF is active (now the default behaviour of IsamDAE). * New data structures were implemented in order to correct the inputs of equations blocks in the XML, text and graph outputs. Before this fix, when two or several derivatives of the same variable appeared in the same equation (as in the simple equation `der(x) + x = 0`), the lower-order derivatives of this variable were ignored. * New examples: several examples have been added, in mechanics, electrodynamics and hydraulics. * Documentation: a comprehensive User and Developer manual is made available.

Modern modeling languages for general physical systems, such as Modelica or Simscape, rely on Differential Algebraic Equations (DAE), i.e., constraints of the form

Unlike Ordinary Differential Equations (ODE, of the form differentiation index and related latent equations—ODE are DAE of index zero for which no latent equation needs to be considered. Prior to generating execution code and calling solvers, the compilation of such languages requires a nontrivial structural analysis step that reduces the differentiation index to a level acceptable by DAE solvers.

Multimode DAE systems, having multiple modes with mode-dependent dynamics and state-dependent mode switching, are much harder to deal with. The main difficulty is the handling of the events of mode change. Unfortunately, the large literature devoted to the numerical analysis of DAEs does not cover the multimode case, typically saying nothing about mode changes. This lack of foundations causes numerous difficulties to the existing modeling tools. Some models are well handled, others are not, with no clear boundary between the two classes. Basically, no tool exists that performs a correct structural analysis taking multiple modes and mode changes into account.

In our work, we developed a comprehensive mathematical approach supporting compilation and code generation for this class of languages. Its core is the structural analysis of multimode DAE systems, taking both multiple modes and mode changes into account. As a byproduct of this structural analysis, we propose well sound criteria for accepting or rejecting models at compile time.

For our mathematical development, we rely on nonstandard analysis, which allows us to cast hybrid systems dynamics to discrete time dynamics with infinitesimal step size, thus providing a uniform framework for handling both continuous dynamics and mode change events.

Modeling languages and tools based on Differential Algebraic Equations (DAE) bring several specific issues that do not exist with modeling languages based on Ordinary Differential Equations. The main problem is the determination of the differentiation index and latent equations. Prior to generating simulation code and calling solvers, the compilation of a model requires a structural analysis step, which reduces the differentiation index to a level acceptable by numerical solvers.

The Modelica language, among others, allows hybrid models with multiple modes, mode-dependent dynamics and state-dependent mode switching. These multimode DAE (mDAE) systems are much harder to deal with. The main difficulties are (i) the combinatorial explosion of the number of modes, and (ii) the correct handling of mode switchings.

The focus of the paper 34 is on the first issue,
namely: How can one perform a structural analysis of an mDAE in all
possible modes, without enumerating these modes? A structural analysis
algorithm for mDAE systems is presented, based on an implicit
representation of the varying structure of an mDAE. It generalizes
J. Pryce's

This method has been implemented in the IsamDAE software. This has
allowed the Hycomes team to evaluate the performance and scalability
of the method on several examples. In particular, it has been possible
to perform the structural analysis of systems with more than 2300
equations and

We introduce a novel framework, termed λDD, that revisits Binary Decision Diagrams from a purely functional point of view. The framework allows to classify the already existing variants, including the most recent ones like Chain-DD and ESRBDD, as implementations of a special class of ordered models. We enumerate, in a principled way, all the models of this class and isolate its most expressive model. This new model, termed λDD-O-NUCX, is suitable for both dense and sparse Boolean functions, and is moreover invariant by negation. The canonicity of λDD-O-NUCX is formally verified using the Coq proof assistant. We furthermore give bounds on the size of the different diagrams: the potential gain achieved by more expressive models can be at most linear in the number of variables n.

We present concise and canonical representations of Boolean functions akin to Binary Decision Diagrams, a versatile data structure with several applications beyond computer science. Our approach is functional: we encode the process that constructs the Boolean function of interest starting from the constant function zero (or False). This point of view makes the data structure more resilient to variable ordering, a well-known problem in standard representations. The experiments on both dense and sparse formulas are very encouraging and show not only a better compression rate of the final representation than all existing related variants but also a lower memory peak.

Set positive invariance is an important concept in the theory of dynamical systems and one which also has practical applications in areas of computer science, such as formal verification, as well as in control theory. Great progress has been made in understanding positively invariant sets in continuous dynamical systems and powerful computational tools have been developed for reasoning about them; however, many of the insights from recent developments in this area have largely remained folklore and are not elaborated in existing literature. This article contributes an explicit development of modern methods for checking positively invariant sets of ordinary differential equations and describes two possible characterizations of positive invariants: one based on the real induction principle, and a novel alternative based on topological notions. The two characterizations, while in a certain sense equivalent, lead to two different decision procedures for checking whether a given semi-algebraic set is positively invariant under the flow of a system of polynomial ordinary differential equations.

We show that the existence of solutions for linear complementarity problems amounts to a covering of the entire space by a set of finite cones defined by the involved vectors as well as the standard basis. We give several full characterizations for the case

The visit of Inigo Incer Romeo, PhD student at U. Berkeley, initially planned in the Summer 2020 had to be postponed to 2021. This visit is supported by a Chateaubriand Fellowship grant of the French Ministry of Foreign Affairs. The topics of the visit is on the use of Contract-based Reasoning to support the design of CPS systems.

The project gathers researchers from three Inria teams (Hycomes, Parkas and Tripop), and from three other research labs in Paris area (ENSTA Paris-Tech, L2S-CNRS and LIX, École Polytechnique).

The main objective of ModeliScale is to advance modeling technologies (languages, compile-time analyses, simulation techniques) for CPS combining physical interactions, communication layers and software components. We believe that mastering CPS comprising thousands to millions of components requires radical changes of paradigms. For instance, modeling techniques must be revised, especially when physics is involved. Modeling languages must be enhanced to cope with larger models. This can only be done by combining new compilation techniques (to master the structural complexity of models) with new mathematical tools (new numerical methods, in particular).

ModeliScale gathers a broad scope of experts in programming language design and compilation (reactive synchronous programming), numerical solvers (nonsmooth dynamical systems) and hybrid systems modeling and analysis (guaranteed simulation, verification). The research program is carried out in close cooperation with the Modelica community as well as industrial partners, namely, Dassault Systèmes as a Modelica/FMI tool vendor, and EDF and Engie as end users.

In 2020, two general meetings have been organized by visioconference, with presentations of the partners on new results related to hybrid systems modeling and verification.

Two PhDs are funded by the ModeliScale IPL. Both started in October 2018:

FUI ModeliScale is a French national collaborative project coordinated by Dassault Systèmes. The partners of this project are: EDF and Engie as main industrial users; DPS, Eurobios and PhiMeca are SME providing mathematical modeling expertise; CEA INES (Chambéry) and Inria are the academic partners. The project started January 2018, for a maximal duration of 42 months. Three Inria teams are contributing to the project : Hycomes, Parkas (Inria Paris / ENS) and Tripop (Inria Grenoble / LJK).

The focus of the project is on the scalable analysis, compilation and simulation of large Modelica models. The main contributions expected from Inria are:

In 2020, the effort has been put on the first objective, and in
particular the improvement of the scalability of the algorithms
implemented in the IsamDAE software
(https://

A coupling of IsamDAE with Dymola (Dassault Système's commercial implementation of the Modelica language) has been implemented by Dassault Systèmes AB (Lund, Sweden), and is currently under test at the time of writing of this activity report.

Khalil Ghorbal was the co-Chair of the NSAD Workshop (satellite of the SPLASH 2020 Event). https://

Abstract domains are a key notion in Abstract Interpretation theory and practice. They embed the semantic choices, data-structures and algorithmic aspects, and implementation decisions. The Abstract Interpretation framework provides constructive and systematic formal methods to design, compose, compare, study, prove, and apply abstract domains. Many abstract domains have been designed so far: numerical domains (intervals, congruences, polyhedra, polynomials, etc.), symbolic domains (shape domains, trees, etc.), but also domain operators (products, powersets, completions, etc.), and have been applied to several kinds of static analyses (safety, termination, probability, etc.) on a variety of systems (hardware, software, neural networks, etc.). The goal of NSAD workshop is to discuss work in progress, recent advances, novel ideas, experiences in the theory, practice, application, implementation, and experimentation related to abstract domains and/or their combination. This year’s edition in particular welcomes abstract domains related and/or applied to analyzing neural networks, dynamical and hybrid systems.

Benoît Caillaud has served on the program committee of FDL'20, a workshop on the domain-specific languages. The workshop took place with both physical (in Kiel, Germany) and virtual attendance (by visioconference).

Benoît Caillaud is head of the Programming Languages and Software Engineering department of IRISA (UMR 6074). Part of his duties has been the preparation of the evaluation of IRISA, planned March 2021.