Taming Past LTL and Flat Counter Systems

  • Stéphane Demri
  • Amit Kumar Dhar
  • Arnaud Sangnier
Part of the Lecture Notes in Computer Science book series (LNCS, volume 7364)


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.


Temporal Logic Counter System Propositional Variable Kripke Structure Path Segment 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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Copyright information

© Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  • Stéphane Demri
    • 1
  • Amit Kumar Dhar
    • 2
  • Arnaud Sangnier
    • 2
  1. 1.LSV, CNRS, ENS Cachan, INRIAFrance
  2. 2.LIAFA, Univ Paris Diderot, Sorbonne Paris Cité, CNRSFrance

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