Taming past LTL and flat counter systems

  • Authors:
  • Stéphane Demri;Amit Kumar Dhar;Arnaud Sangnier

  • Affiliations:
  • LSV, CNRS, ENS Cachan, INRIA, France;LIAFA, Univ Paris Diderot, Sorbonne Paris Cité, CNRS, France;LIAFA, Univ Paris Diderot, Sorbonne Paris Cité, CNRS, France

  • Venue:
  • IJCAR'12 Proceedings of the 6th international joint conference on Automated Reasoning
  • Year:
  • 2012

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Abstract

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 pasttime 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.