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The default language is French.
But the lectures may be given in English if attended by non French-speaking students.
Nowadays, it is of the highest importance to use formal methods in order to increase the reliability of critical systems.
In this introductory course on verification of discrete systems, we concentrate in particular on model checking techniques.
We will describe various models used to define systems: transition systems enriched with various data structures (variables, channels, ...) and which can be composed with several synchronization mechanisms.
We will also cover specification languages that are used to express properties to be checked on our systems: temporal logics (linear or branching), first-order or monadic second-order logic, ...
We will study expressivity, decidability and complexity properties of our models and specification languages.
We will also cover abstraction/refinement techniques and (bi)simulation relations used to relate various abstraction levels.
Algorithmic aspects of model checking will be investigated and we will stress efficient techniques such as binary decision diagrams (BDDs) or bounded model checking.
Detailed description and Lecture notes
| Date | Topics covered | Documents |
| 2019/09/20 | Introduction & motivation
Models: Transition systems (Kripke structures), variables, synchronized products, Rendez-vous,
shared variables, atomicity, asynchronous communication, FIFO channels | Slides |
| 2019/09/27 | Specification: introduction, examples, temporal structures, first-order vs temporal logics
Linear temporal logics: definitions, examples, model checking | Slides |
| 2019/10/04 | linear vs branching specifications, Branching specifications.
MSO, CTL*, CTL: definitions, examples, model checking | Slides |
| 2019/10/11 | Cancelled | |
| 2019/10/18 | PTIME Model checking algorithm for CTL and for CTL with fairness | Slides |
| 2019/10/25 | Büchi automata: definition, examples, main properties, generalized acceptance, unambiguity
Sequential Büchi transducers: definition and examples
Sequential Büchi transducer for basic LTL formulas | Slides |
| 2019/11/08 | Construction of a sequential Büchi transducer for an arbitrary LTL formula
Satisfiability and Model checking for LTL: decidability and complexity
PSPACE model checking algorithm for CTL* | Slides |
| 2019/11/15 | Büchi emptiness check | Slides |
| 2019/11/22 | Partial-order reduction | Slides |
| 2019/11/29 | Binary decision diagrams | Slides |
| 2019/12/06 | Petri nets | Slides
Homework10
Exercises |
| 2019/12/13 | Petri nets | Slides
Homework11
Exercises |
| 2019/12/20 | Petri nets, Pushdown systems | Slides
Homework12
Exercises |
| 2020/01/10 | Abstraction/refinement | Slides
Homework9
Exercises |
Finite Automata
First-order logic
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Principles of Model Checking. Christel Baier and Joost-Pieter Katoen. MIT Press, 2008. Systems and Software Verification. Model-Checking Techniques and Tools. B. Bérard, M. Bidoit, A. Finkel, F. Laroussinie, A. Petit, L. Petrucci, Ph. Schnoebelen. Springer, 2001.
Also available in french: Vérification de logiciels : Techniques et outils du model checking. Coordonné par Ph. Schnoebelen. Vuibert, 1999.
Model Checking. E.M. Clarke, O. Grumberg, D. Peled. MIT Press, 1999. Temporal Verification of Reactive Systems - Safety. Zohar Manna and Amir Pnueli. Springer-Verlag, 1995.
The Temporal Logic of Reactive and Concurrent Systems - Specification. Zohar Manna and Amir Pnueli. Springer-Verlag, 1992.
| Paul Gastin | PR | ENS Paris-Saclay | LSV |
| Stefan Schwoon | MC | ENS Paris-Saclay | LSV |
| Nathan Thomasset | PhD | ENS Paris-Saclay | LSV |
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