In charge: Stefan Schwoon (LSV, ENS Cachan).

Thomas Chatain, Marie Fortin, Philippe Schnoebelen, Stefan Schwoon.

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.

Here are the planned contents for the first half of the course (which might change slightly):

This years's mid-term exam: subject, with solutions.

Final exam: subject, solutions

Last years's subjects for mid-term exams: 2015, 2014.

Finite Automata
First-order logic

• 1-18: Tree automata and applications
• 2-8-1: Non-sequential theory of distributed systems
• 2-8-2: Foundations of real time and hybrid systems
• 2-9-1: Mathematical foundations of the theory of infinite transition systems
• 2-9-2: Algorithmic verification of programs
• 2-20-1: Game theoretic techniques in computer science

• Ph. Schnoebelen. The Complexity of Temporal Logic Model Checking. In AiML’02, pages 393-436. King’s College Publication, 2003. Invited paper.
• 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.

• 2015-2016
• 2014-2015
• 2013-2014
• 2012-2013
• 2011-2012