Taming Past LTL and Flat Counter Systems

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

1 LSV - Laboratoire Spécification et Vérification
2 CNRS - Centre National de la Recherche Scientifique
3 LIAFA - Laboratoire d'informatique Algorithmique : Fondements et Applications

Reachability and LTL model-checking problems for flat counter systems are known to be decidable but whereas the reachability problem can be shown in NP, the best known complexity upper bound for the latter problem is made of a tower of several exponentials. Herein, we show that the problem is only NP-complete even if LTL admits past-time operators and arithmetical constraints on counters. Actually, the NP upper bound is shown by adequately combining a new stuttering theorem for Past LTL and the property of small integer solutions for quantifier-free Presburger formulae. Other complexity results are proved, for instance for restricted classes of flat counter systems.

Mots clés: model-checking; counter machine; linear-time temporal logic LTL; past-time temporal operator; Presburger arithmetic; arithmetical constraint; complexity; NP; small solutions; small ultimately periodic model

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

Stéphane Demri, Amit Kumar Dhar, Arnaud Sangnier. Taming Past LTL and Flat Counter Systems. 6th International Joint Conference, IJCAR 2012, Bernhard Gramlich; Dale Miller; Uli Sattler, Jun 2012, Manchester, United Kingdom. pp.179-193, ⟨10.1007/978-3-642-31365-3_16⟩. ⟨hal-03202398⟩