Equivalence Between Model-Checking Flat Counter Systems and Presburger Arithmetic

Stéphane Demri (1, 2) , Amit K Kumar Dhar (3) , Arnaud Sangnier (4)

1 LSV - Laboratoire Spécification et Vérification
2 CNRS - Centre National de la Recherche Scientifique
3 IIIT Allahabad - Indian Institute of Information Technology Allahabad
4 IRIF (UMR_8243) - Institut de Recherche en Informatique Fondamentale

We show that model-checking flat counter systems with the branching-time temporal logic CTL* extended with arithmetical constraints on counter values has the same worst-case complexity as the satisfiability problem for Presburger arithmetic. The lower bound already holds with strong restrictions: the logical language uses only the temporal operator EF and no arithmetical constraints, and the guards on the transitions are made of linear constraints. This work complements our understanding of model-checking flat counter systems with linear-time temporal logics, such as LTL, for which the problem is already known to be (only) NP-complete with guards restricted to the linear fragment.

Mots clés: counter machine; flatness; Presburger arithmetic; temporal logic; model-checking; linear-time temporal logic LTL

Domaines: Informatique [cs]; Logique en informatique [cs.LO]

Stéphane Demri, Amit K Kumar Dhar, Arnaud Sangnier. Equivalence Between Model-Checking Flat Counter Systems and Presburger Arithmetic. Theoretical Computer Science, 2017, 735, pp.2-23. ⟨10.1016/j.tcs.2017.07.007⟩. ⟨hal-03192244⟩