Parisian Master of Research in Computer Science
Master Parisien de Recherche en Informatique (MPRI)

Basics of Verification (60h, 6 ECTS)

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


Research internships


The default language is French.
But the lectures may be given in English if attended by non French-speaking students.

Motivations and main objectives

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

Lecture Notes of Etienne Lozes (very unstable version, will be updated regularly). Please do not hesitate to send me your comments.

Home Assignment

Date Topics covered
2014/09/16 Introduction
Models: transition systems, variables, synchronized products, rendez-vous
Specification: introduction, linear vs branching specifications, FO and TL: definitions and examples, linear model checking, branching specifications, MSO, CTL*
2014/09/23 ...
Mutual exclusion algorithms, Handshake with data exchange, Needham-Schroeder protocol
2014/09/30 mu-calculus...
CTL, PTIME model checking algorithm for CTL
2014/10/07 mu-calculus...
2014/10/14 Büchi automata...
CTL PTIME-complete, fair CTL Slides
2014/11/18 Emptiness test for Büchi automata (Slides)
Binary decision diagrams (Slides)
2014/12/02 Partial-order reduction (Slides)
2014/12/09 Petri nets part 1 (Slides)
2014/12/16 Petri nets part 2 (Slides)
Abstraction/refinement (Slides)


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.
Since the second homework did not take place, the final mark will be (H1+2E1+2E2)/5.

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.

Date Type Topics and comments
2014/11/10 E1: midterm exam Exam on the first half of the course.
2015/01/13 E2: final exam, solutions Exam on the second half of the course.

Exams from previous years

Concerning the second part of the course, the exams and solutions of previous years can be found in the pages for previous editions of the course (see the links at the bottom of the page), except for 2013-14, which are here (exam) and here (solutions).


Finite Automata.

Related courses

  • 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.


Étienne LozesMCENS CachanLSV
Thomas ChatainMCENS CachanLSV
Stefan SchwoonMCENS CachanLSV
Daniel StanPhDENS CachanLSV

Previous Years

Universités partenaires Université Paris-Diderot
Université Paris-Saclay
ENS Cachan École polytechnique Télécom ParisTech
Établissements associés Université Pierre-et-Marie-Curie CNRS INRIA CEA