M. Avanzini & E. Lozes

Logique avancée

With this lecture we invite you to discover some close links between logic and automata.

S2 3 ECTS 24h OPT EN Site web M. Avanzini, E. Lozes


It is necessary to have followed a course in logic having dealt with propositional logic and the calculus of predicates. Familiarity with automata on finite words is desirable (these will be recalled very briefly). Mastery of a programming language is needed for mini-projects.

One half of the lecture will be in english, the other half will be either in english or in french, on request.


  • mini-project on regular expressions matching: 1/4
  • mini-project on automata learning: 1/4
  • final examination: 1/2

Course Material

Course notes and corrected exercise sheets will be provided online.


In the early 60s, Büchi, Elgot and Trakhtenbrot formulated a correspondence between regular finite word languages and those described by weak second-order monadic logic. Beside the nice mathematical theory, this correspondence has several applications. An example of application is a family of decision procedures for some logical formalisms that are particularly useful for system specifications. Another example is a method to synthesize a constant space algorithm from a problem specification.

The Büchi-Elgot-Trakhtenbrot correspondence extends to infinite words and monadic second order logic. It also extends to the languages of finite and infinite trees, allowing to completely automate reasoning for many useful logics in checking programs such as Presburger arithmetic, LTL, CTL, CTL* temporal logics, modal mu-calculus, etc.

The purpose of this course is to discover some of the simplest of these correspondences between automata and logics in a rather practical approach. Along with the nice theory, you will experiment concretely with the MONA tool and you will have to work out two rather guided programming assignments, one of which deals with Dana Angluin L* algorithm for automata learning.

Discussed subjects

  • automata learning
  • automata synthesis
  • monadic second-order logic
  • Presburger arithmetic
  • automata on infinite words
  • linear-time temporal logic
  • tree automata