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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.
The full lecture notes of the first half of the semester are available here.
| Date | Type | Topics covered |
| 2011/09/14 | Lecture | Introduction
Models: transition systems, variables, synchronized products, Rendez-vous, shared variables, atomicity, asynchronous communication with channels |
| 2011/09/21 | Exercises | Mutual exclusion algorithms, Handshake with data exchange, Needham-Schroeder protocol, Channel systems |
| 2011/09/28 | Lecture | Specification: introduction, FO and TL: definitions and examples, Expressivity, Separation |
| 2011/10/05 | Exercises | Specification, LTL, LTL with past |
| 2011/10/12 | Lecture | Ehrenfeucht-Fraïssé games for temporal logics |
| 2011/10/19 | Exercises | Ehrenfeucht-Fraïssé Games |
| 2011/10/26 | Lecture | Büchi automata and Büchi transducers: definitions, examples and main properties
Construction of a Büchi transducer from an LTL formula
Satisfiability and Model checking for LTL: decidability and complexity |
| 2011/11/02 | Exercises | Büchi automata and transducers |
| 2011/11/09 | Lecture | Branching time specifications
PSPACE model checking algorithm for CTL*
PTIME model checking algorithm for CTL |
| 2011/11/16 | Exercises | TL(X), CTL*, and CTL |
| 2011/12/07 | Lecture | Petri nets, unfoldings |
| 2011/12/07 | Lecture | Petri nets, coverability graph |
2012/01/04
2012/01/11 | Exercises | Petri nets: modeling, model-checking, unfoldings, coverability graphs, and vector addition systems |
| 2012/01/18 | Lecture | Binary decision diagrams |
| 2012/01/25 | Exercises | Binary decision diagrams |
| 2012/02/01 | Lecture | Pushdown systems |
| 2012/02/08 | Exercises | Pushdown Systems |
| 2012/02/15 | Lecture | Partial-order reductions |
| 2012/02/22 | Exercises | Partial-Order Reduction |
There will be 2 written exams (E1 and E2) and 2 home assignments (H1 and H2).
The final mark will be (H1+2E1+H2+2E2)/6.
The examination questions will be in French and/or in English depending on the requests.
Students may write their answers in French or in English.
1-2: Automates avancés et applications
1-18: Automates d'arbres et applications
2-8: Fondements pour la vérification des systèmes temps-réel
2-9: Vérification de systèmes dynamiques et paramétrés
2-16: Modélisation par automates finis
2-20-1: Jeux pour la théorie des automates, la vérification et l'internet.
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 | PU | ENS Cachan | LSV |
| Sylvain Schmitz | MC | ENS Cachan | LSV |
| Stefan Schwoon | MC | ENS Cachan | LSV |
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