Eric Goubault

Professor of Computer Science, École Polytechnique

Office: Room 2153, LIX - UMR 7161
École Polytechnique
1 rue Honoré d'Estienne d'Orves
Bâtiment Alan Turing
91120 Palaiseau

E-mail : Eric Goubault at polytechnique dot edu

Research

Publications

Teaching

Publications

Books

Directed Algebraic Topology and Concurrency Springer International Publishing, 2016. Lisbeth Fajstrup, Éric Goubault, Emmanuel Haucourt, Samuel Mimram, and Martin Raussen. [ bib | DOI |

Peer-reviewed Conferences

A Simplicial Complex Model for Dynamic Epistemic Logic to study Distributed Task Computability, Eric Goubault, Jérémy Ledent and Sergio Rajsbaum, Gandalf 2018.
Discrete Choice in the Presence of Numerical Uncertainties, Eva Darulova, Eric Goubault, Sylvie Putot, Debasmita Lohar, Proceedings (to appear in IEEE TCAD) of the International Conference on Embedded Software, EMSOFT 2018.
Inner and Outer Approximating Flowpipes for Delay Differential Equations, Eric Goubault, Sylvie Putot and Lorenz Sahlmann, Proceedings of the 30th International Conference on Computer Aided Verification, CAV 2018, slides.
Reachability Analysis for Time-triggered Hybrid Systems, The Platoon Benchmark, François Bidet, Eric Goubault and Sylvie Putot, Work in Progress, 11th Conference on Intelligent Computer Mathematics, CICM 2018.
On the impossibility of detecting concurrency, Eric Goubault, Jérémy Ledent and Samuel Mimram, brief announcement, DISC 2018.
A simplicial complex model for epistemic logic, Eric Goubault, Jérémy Ledent and Sergio Rajsbaum, short paper, AiML 2018.
Forward inner-approximated reachability of non-linear continuous systems, Eric Goubault and Sylvie Putot, Proceedings of the 20th ACM International Conference on Hybrid Systems: Computation and Control, HSCC 2017, slides, prototype (reproductibility package) .
A Topological Method for Finding Invariant Sets of Switched Systems, Laurent Fribourg, Eric Goubault, Sameh Mohamed and Sylvie Putot, Proceedings of the 19th ACM International Conference on Hybrid Systems: Computation and Control, HSCC 2016.
Uncertainty Propagation using Probabilistic Affine Forms and Concentration of Measure Inequalities, Olivier Bouissou, Eric Goubault, Sylvie Putot, Aleksandar Chakarov and Sriram Sankaranarayanan, Proceedings of the 22nd International Conference on Tools and Algorithms for the Construction and Analysis of Systems, TACAS 2016.
The Directed Homotopy Hypothesis, Jérémy Dubut, Eric Goubault and Jean Goubault-Larrecq, CSL 2016.
Bisimulations and Unfolding in P-Accessible Categorical Models, Jérémy Dubut, Eric Goubault and Jean Goubault-Larrecq, CONCUR 2016.
From Geometric Semantics to Asynchronous Computability, Eric Goubault, Samuel Mimram, and Christine Tasson, In Yoram Moses, editor, Distributed Computing, volume 9363 of Lecture Notes in Computer Science, pages 436--451. Springer Berlin Heidelberg, 2015. [ bib | DOI | pdf | slides | http ]
A scalable algebraic method to infer quadratic invariants of switched systems, Xavier Allamigeon, Stephane Gaubert, Eric Goubault, Sylvie Putot and Nikolas Stott, Proceedings of the ACM SIGBED International Conference on Embedded Software EMSOFT 2015 (best paper award).
A Topological Method for Finding Invariant Sets of Continuous Systems, Laurent Fribourg, Eric Goubault, Sameh Mohamed, Marian Mrozek and Sylvie Putot, Proceedings of the 9th International Workshop on Reachability Problems RP 2015, LNCS volume 9328, pp 63-75, 2015.
Natural Homology, Jérémy Dubut, Eric Goubault and Jean Goubault-Larrecq, ICALP 2015.
Finding Non-Polynomial Positive Invariants and Lyapunov Functions for Polynomial Systems through Darboux Polynomials, Eric Goubault, Jacques-Henri Jourdan, Sylvie Putot and Sriram Sankaranarayanan, Proceedings of American Control Conference ACC 2014.
Inner approximated reachability analysis, Eric Goubault, Michel Kieffer, Olivier Mullier and Sylvie Putot, Proceedings of Hybrid Systems: Computation and Control HSCC 2014, ACM, 2014.
Robustness analysis of finite precision implementations, Eric Goubault and Sylvie Putot, extended version, Proceedings of Asian Symposium on Programming Languages and Systems APLAS 2013, LNCS volume 8301, pp 50-57, 2013, slides .
Static Analysis of Programs with Imprecise Probabilistic Inputs, Assale Adje, Olivier Bouissou, Eric Goubault, Jean Goubault-Larrecq, Sylvie Putot, Proceedings of Verified Software: Theories, Tools and Experiments VSTTE'13, LNCS volume 8164, 2013.
A Geometric View of Partial Order Reduction, Éric Goubault, Tobias Heindel, and Samuel Mimram, Electronic Notes in Theoretical Computer Science, 298(0):179–195, 2013. Proceedings of the Twenty-ninth Conference on the Mathematical Foundations of Programming Semantics, MFPS XXIX. [ bib | DOI | http ]
Modular Static Analysis with Zonotopes, Eric Goubault, Sylvie Putot and Franck Védrine, Proceedings of Static Analysis Symposium SAS'12, Deauville, France, LNCS volume 7460, pp 24-40, slides
An Accurate Join for Zonotopes, Preserving Affine Input/Output Relations, Eric Goubault, Tristan Le Gall and Sylvie Putot, Proceedings of the Workshop on Numerical and Symbolic Abstract Domains, NSAD'12, Electronic Notes in Theoretical Computer Science, volume 287, pp 65-76, 2012
Design of fixed-point embedded systems (DEFIS) French ANR project, D. Menard, R. Rocher, O. Sentieys, N. Simon, L.-S. Didier, T. Hilaire, B. Lopez, E. Goubault, S. Putot, F. Védrine, A. Najahi, G. Revy, L. Fangain, C. Samoyeau, F. Lemonnier, C. Clienti, Proceedings of the Conference on Design and Architectures for Signal and Image Processing, DASIP 2012, Karlsruhe, Germany
Trace Spaces: An Efficient New Technique for State-Space Reduction, Lisbeth Fajstrup, Éric Goubault, Emmanuel Haucourt, Samuel Mimram, and Martin Raussen, In Helmut Seidl, editor, Programming Languages and Systems, volume 7211 of Lecture Notes in Computer Science, page 274–294. Springer Berlin Heidelberg, 2012. [ bib | DOI | arXiv | slides | http ]
Formal Relationships Between Geometrical and Classical Models for Concurrency, Éric Goubault and Samuel Mimram, Electronic Notes in Theoretical Computer Science, 283(0):77-109, 2012. Proceedings of the workshop on Geometric and Topological Methods in Computer Science (GETCO). [ bib | DOI | arXiv | http ]
Rigorous Evidence of Freedom from Concurrency Faults in Industrial Control Software, Richard Bonichon, Géraud Canet, Loic Correnson, Eric Goubault, Emmanuel Haucourt, Michel Hirschowitz, Sébastien Labbé, and Samuel Mimram, In Francesco Flammini, Sandro Bologna, and Valeria Vittorini, editors, Computer Safety, Reliability, and Security, volume 6894 of Lecture Notes in Computer Science, page 85–98. Springer Berlin Heidelberg, 2011. [ bib | DOI | http ]
Static Analysis of Finite Precision Computations, Proceedings of Verification, Model Checking and Abstract Interpretation VMCAI'11, Austin, Texas, LNCS volume 6530, pp. 232-247, slides, Eric Goubault and Sylvie Putot
Policy Iteration within Logico-Numerical Abstract Domains, Eric Goubault, Pascal Sotin, Bertrand Jeannet and Franck Védrine, ATVA, 2011
Abstract Interpretation Meets Convex Optimization, Eric Goubault, Thomas Martin Gawlitza, Helmut Seidl, Assalé Adjé and Stéphane Gaubert, WING, 2010, to be published, 2011.
A Logical Product to Zonotope Intersection, Khalil Ghorbal, Eric Goubault and Sylvie Putot, Proceedings of Computer Aided Verification CAV'10, Edinburgh, Scotland, LNCS volume 6174, pp. 212-226
Future Path-Components in Directed Algebraic Topology, Eric Goubault, Emmanuel Haucourt and Sanjeevi Krishnan Mathematical Foundations of Programming Semantics, 2010
The Tropical Double Description Method, Eric Goubault, Xavier Allamigeon and Stéphane Gaubert, STACS 2010, presented in Nancy.
Coupling Policy Iteration with Semi-Definite Relaxation to Compute Accurate Numerical Invariants in Static Analysis, Eric Goubault, Assalé Adjé and Stéphane Gaubert
long version ESOP 2010, presented in Cyprus; long version in Logical Methods in Computer Science, 2011.
Towards an Industrial Use of FLUCTUAT on Safety-Critical Avionics Software,David Delmas, Eric Goubault, Sylvie Putot, Jean Souyris, Karim Tekkal and Franck Védrine, Proceedings of 14th International Workshop on Formal Methods for Industrial Critical Systems FMICS'09, LNCS volume 5825, pp. 53-69
slides, the movies shown: intro: behaviour of Householder algorithm for sqrt, Householder analysed by FLUCTUAT, analysis of an algorithm for the arctangent

HybridFluctuat: A Static Analyzer of Numerical Programs within a Continuous Environment, Olivier Bouissou, Eric Goubault, Sylvie Putot, Karim Tekkal and Franck Védrine, Proceedings of Computer Aided Verification CAV'09, Grenoble, France, LNCS volume 5649, pp. 620-626
The Zonotope Abstract Domain Taylor1+, Khalil Ghorbal, Eric Goubault and Sylvie Putot, Proceedings of Computer Aided Verification CAV'09, Grenoble, France, LNCS volume 5649, pp. 627-633
Space Software Validation using Abstract Interpretation, O. Bouissou, E. Conquet, P. Cousot, R. Cousot, J. Feret, K. Ghorbal, E. Goubault, D. Lesens, L. Mauborgne, A. Mine, S. Putot and X. Rival, Proceedings of the Int. Space System Engineering Conference, Data Systems in Aerospace DASIA'09, Istambul, Turkey.
Computing the smallest fixpoint of nonexpansive mappings arising in game theory and static analysis of programs, Eric Goubault, Assalé Adé and Stéphane Gaubert, Proceedings of MTNS'08, presented at Virginia Tech, july 2008
Inferring Min and Max Invariants Using Maxplus Polyhedra, Eric Goubault, Xavier Allamigeon and Stéphane Gaubert, Proceedings of SAS'08, presented in Valencia, july 2008
Static Analysis of the Accuracy in Control Systems : Principles and Experiments, Eric Goubault, Sylvie Putot, Philippe Baufreton and Jean Gassino, Proceedings of 12th International Workshop on Formal Methods for Industrial Critical Systems FMICS'07, Berlin, Germany, LNCS volume 4916, pp. 3-20
Under-Approximations of Computations in Real Numbers Based on Generalized Affine Arithmetic, Eric Goubault and Sylvie Putot, Proceedings of Static Analysis Symposium SAS'07, Kongens Lyngby Denmark, LNCS volume 4634, pp. 137-152
Static Analysis by Policy Iteration on Relational Domains , Eric Goubault, Stéphane Gaubert, Sarah Zennou and Ankur Taly, Proceedings of ESOP'07, presented at Braga, Portugal
Static Analysis of Numerical Algorithms, Eric Goubault and Sylvie Putot, Proceedings of Static Analysis Symposium SAS'06, Seoul, LNCS volume 4134, pp. 18-34
Some future challenges in the validation of control systems, Eric Goubault, Matthieu Martel and Sylvie Putot, Proceedings of Embedded Real-Time Systems ERTS'06, Toulouse
A practical application of geometric semantics to the static analysis of concurrent programs, Eric Goubault and Emmanuel Haucourt, Proceeding of CONCUR'05, presented in San Francisco, august 2005
A policy iteration algorithm for computing fixed points in static analysis of programs, Alexandru Costan, Stephane Gaubert, Eric Goubault, Matthieu Martel and Sylvie Putot, Proceedings of Computer Aided Verification CAV'05, Edinburgh, LNCS volume 3576, pp. 462-475
Weakly relational domains for floating-point computation analysis, Eric Goubault and Sylvie Putot, Proceedings of the workshop on Numerical and Symbolic Abstract Domains NSAD'05, Paris (affiliated event of VMCAI'05)
Static Analysis-Based Validation of Floating-Point Computations, Eric Goubault, Matthieu Martel and Sylvie Putot, Proceedings of Dagstuhl Seminar Numerical Software with Result Verification 2003, LNCS volume 2991, pp 306-313
Asserting the Precision of Floating-Point Computations: a Simple Abstract Interpreter, Eric Goubault, Matthieu Martel, and Sylvie Putot, Proceedings of ESOP'02, Grenoble, LNCS volume 2305, pp 209-212
Cubical Sets are Generalized Transition Systems, Eric Goubault, Presented at CMCIM'02 (associated with Concur, Brno, Cech Republic)
Static Analyses of Floating-Foint Operations , Eric Goubault, presented at SAS'01 (La Sorbonne)
A Simple Abstract Interpreter for Threat Detection and Test Case Generation , Eric Goubault, Dominique Guilbaud, Anne Pacalet, Basile Starynkévitch and Franck Védrine, presented at WAPATV'01 (associated with ICSE'01, Toronto)
Order-Theoretic, Geometric and Combinatorial Models of Intuitionistic S4 Proofs, Eric Goubault, Jean Goubault-Larrecq, presented at FLoC'99, IMLA workshop (associated with LICS, Trento)
Detecting Deadlocks in Concurrent Systems, Eric Goubault, Lisbeth Fajstrup and Martin Raussen, (long version, CEA report) Presented at CONCUR'98 (Nice)
Optimal Implementation of Wait-Free Binary Relations , Eric Goubault, presented at CAAP'97 (Lille)
Durations for Truly-Concurrent Transitions , Eric Goubault, presented at ESOP'96 (Linkeping)
A Semantic View on Distributed Computability and Complexity , Eric Goubault, presented at the Imperial College Workshop'96 (Oxford).
The Dynamics of Wait-Free Distributed Computations , Eric Goubault, presented at the Logique et Calculs Workshop'96 (Marseille); also LIENS report (Ecole Normale Supérieure)
Schedulers as Abstract Interpretations of Higher-Dimensional Automata , Eric Goubault, presented at PEPM'95 (La Jolla)
Domains of Higher-Dimensional Automata , Eric Goubault, presented at CONCUR'93 (Hildesheim).
Semantics and Analyses of Linda-based Languages , Eric Goubault, Regis Cridlig, presented at WSA'93 (Padova).
Homology of Higher-Dimensional Automata , Eric Goubault and Thomas Jensen, presented at CONCUR'92 (New-York).
A Lattice for the Abstract Interpretation of Term Graph Rewriting Systems , Eric Goubault, Chris Hankin, presented at SemaGraph'91 (Nijmegen), also Chapter 10 of "Term Graph Rewriting", Wiley, 1993
Abstract Reduction: Towards a Theory via Abstract Interpretation , Eric Goubault, Marko van Eekelen, Chris Hankin, Eric Nocker, presented at SemaGraph'91 (Nijmegen), also as Chapter 9 of "Term Graph Rewriting", Wiley, 1993
Low bit-rate coder using hierarchical motion compensation and low-complexity vector quantization, Eric Goubault, C. Raimondo, C. Galand, E. Lancon, and J. Menez, presented at ICASSP, Toronto, Canada, 1991

Journal papers

Directed homology theories and Eilenberg-Steenrod axioms, Jérémy Dubut, Eric Goubault and Jean Goubault-Larrecq, Applied Categorical Structures 25(5), 2017.
A fast method to compute disjunctive quadratic invariants of numerical programs, Xavier Allamigeon, Stéphane Gaubert, Eric Goubault, Sylvie Putot and Nikolas Stott, ACM Transactions on Embedded Computing Systems, TECS, vol 16(5), also presented at EMSOFT 2017.
Directed Homotopy in Non-Positively Curved Spaces, Éric Goubault and Samuel Mimram, Submitted, 2016. [ bib |
Geometric and Combinatorial Views on Asynchronous Computability, Éric Goubault, Samuel Mimram, and Christine Tasson, Submitted, 2016. [ bib |
A scalable algebraic method to infer quadratic invariants of switched systems, Xavier Allamigeon, Stephane Gaubert, Eric Goubault, Sylvie Putot and Nikolas Stott, extended version of the EMSOFT 2015 paper, ACM Transactions on Embedded Computing Systems (TECS), Vol 15(4), 2016.
A zonotopic framework for functional abstractions, Eric Goubault and Sylvie Putot, preprint, Formal Methods in System Design, 47(3), pp 302-360, 2016.
Iterated Chromatic Subdivisions are Collapsible, Eric Goubault, Samuel Mimram, and Christine Tasson, Applied Categorical Structures, page 1–42, 2014. [ bib | DOI | http ]
General Inner Approximation of Vector-valued Functions, Olivier Mullier, Eric Goubault, Michel Kieffer and Sylvie Putot, Reliable Computing, volume 18, pp 117-143, 2013.
A generalization of p-boxes to affine arithmetic, Olivier Bouissou, Eric Goubault, Jean Goubault-Larrecq and Sylvie Putot, Computing, volume 94, nb 2-4, pp 180-201, 2012.
Covering Space Theory for Directed Topology Eric Goubault, Emmanuel Haucourt and Sanjeevi Krishnan, Theory and Applications of Categories, 2009
Components of the Fundamental Category II, Eric Goubault and Emmanuel Haucourt, Journal of Applied Categorical Structures, 2007
Components of the Fundamental Category, E. Goubault, L. Fajstrup, E. Haucourt, M. Raussen, published in Applied Categorical Structures (2004). Also Report R-2003-02 from Aalborg University
On the Geometry of Intuitionistic S4 Proofs, E. Goubault and J. Goubault-Larrecq, published in "Homomogy, Homotopy and Applications" (2003)
Some Geometric Perspectives in Concurrency Theory, Eric Goubault, published in "Homology, Homotopy and Applications" (2003)
Topological Deformation of Higher Dimensional Automata, E. Goubault and P. Gaucher published in "Homology, Homotopy and Applications" (2003), also in arXiv:math.AT/010760
Geometry and Concurrency: A User's Guide (also in html form), Eric Goubault, Mathematical Structures in Computer Science, Volume 10, Number 4, August 2000
Algebraic Topology and Concurrency, Eric Goubault, Lisbeth Fajstrup and Martin Raussen, Report RR-98-2008 of the Department of Mathematical Sciences, Aalborg University; presented at Mathematical Foundations of Computer Science'98 (London); also Theoretical Computer Science (2005)
Groupes Ext1 et déformations de représentations de certaines algebres de Lie nilpotentes, Eric Goubault and Claude Le Bris, Bulletin des Sciences Mathematiques (1992)

Patents

Improved method for coding digital data using vector quantizing techniques and device for implementing said method , European Patent for IBM France (1992)
A vector quantizing method for coding signals and system for implementing said method , European and US Patent for IBM France (1991)

Preprints

On directed homotopy equivalences and a notion of directed topological complexity, Eric Goubault, arXiv.math:1709.05702, 2017.
A simplicial complex model of dynamic epistemic logic for fault-tolerant distributed computing, Eric Goubault and Sergio Rajsbaum, arXiv.CS:1703.11005, 2017.
Models of fault-tolerant distributed computation via dynamic epistemic logic, Eric Goubault and Sergio Rajsbaum, arXiv.CS:1704.07883, 2017.
Formal Verification of Station Keeping Maneuvers for a Planar Autonomous Hybrid System, Benjamin Martin, Khalil Ghorbal, Eric Goubault and Sylvie Putot, Proceedings of the Formal Verification of Autonomous Vehicles workshop, FVAV 2017.
Robustness analysis of finite precision implementations, Eric Goubault and Sylvie Putot, extended version of our APLAS 2013 paper, Sept 2013
Perturbed affine arithmetic for invariant computation in numerical program analysis, Eric Goubault and Sylvie Putot, July 2008
Qu'est-ce que la sureté des systèmes programmés? (french) doc, html, Les clefs du CEA, numéro 42, automne 1999

Presentations

A dynamic epistemic logic semantics for fault-tolerant distributed task computability, Eric Goubault, Jérémy Ledent and Sergio Rajsbaum, informal presentation, CiE 2018.
To be completed

HDR

Géométrie du parallélisme

PhD Thesis

Geometric Models for Concurrency