Decidable first-order transition logics for PA-processes

  • Authors:
  • Denis Lugiez;Philippe Schnoebelen

  • Affiliations:
  • Lab. d'Informatique Fondamentale de Marseille (LIF), Univ. Aix-Marseille 1 & CNRS, France;Lab. Spécification et Vérification (LSV), ENS de Cachan & CNRS, France

  • Venue:
  • Information and Computation
  • Year:
  • 2005

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Abstract

We show the decidability of model checking PA-processes against several first-order logics based upon the reachability predicate. The main tool for this result is the recognizability by tree automata of the reachability relation. The tree automata approach and the transition logics we use allow a smooth and general treatment of parameterized model checking for PA. This approach is extended to handle a quite general notion of costs of PA-steps. In particular, when costs are Parikh images of traces, we show decidability of a transition logic extended by some form of first-order reasoning over costs.