Utilisation des langages d'arbres pour la modélisation et la vérification des systèmes à états infinis

This document presents different tools to represent and manipulate infinitsets of tree tuples called tree tuple languages. We choose logic programming as formalismto describe tree tuple languages (i.e relations) and logic program transformation techniquesfor computing operations on them. In a first step we study a class of relation closed underusual sets operations, the class of pseudo-regular relations. Thanks to a link between logicprograms and rewrite systems, we define classes of conditionnal term rewriting systemthe transitive closure of which is a pseudo-regular relation. We apply this result to givea decidable class of first order formulae based on the joinability predicate↓R where R isa pseudo-regular term rewrite system. Then we extend this result to the second order,the second order variables are interpreted as relations. From an original generic algorithmthat decides the satisfiability of positive second order formulae under some conditions, werepresent one particular instance in a conditionnal term rewriting system. We show thatthis work can be used to automatically synthetize a program.In a last step, we use over approximations to test inconsistances tests. For this weuse a non regular logic programs which have a decidable emptiness test to make theover-approximation. We finally apply this method to verify cryptographic protocols.