Sur la vérification de systèmes infinis

Abstract : This thesis is about the verification problem of systems having an infinite number of states. These systems can be described by several formalisms like process algebras or automata together with unbounded data-structures (push-down automata, Petri nets or communicating finite-state machines). In a first part of the thesis we study the characterization of classes of infinite-state systems and properties for which the verification problem is decidable. First, we consider the complexity of the verification problem of the linear-time mu-calculus for Petri nets. Then, we define temporal logics which allow to express non-regular properties containing linear constraints on the number of occurrences of events. These logics are more expressive than known logics in this domain. We show in particular that the verification problem of a logic which is more expressive than the linear-time mu-calculus is decidable for classes of systems like push-down automata and Petri nets. A second part of the thesis is dedicated to communicating finite-state machines. Their verification problem is in general undecidable. We apply the symbolic analysis principle to these systems. We propose finite structures which allow to represent and manipulate infinite sets of configurations of these systems. These structures allow to calculate the exact effect of a repeated execution of every circuit in the transition graph of the system. Thus, every circuit of the transition graph of the system can be considered as a new "transition" of the system. We use this result to accelerate the computation of the set of reachable states of a system in order to increase the chance of termination.
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Peter Habermehl. Sur la vérification de systèmes infinis. Autre [cs.OH]. Université Joseph-Fourier - Grenoble I, 1998. Français. ⟨tel-00004890⟩

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