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Taming past LTL and flat counter systems. (English) Zbl 1358.68186
Gramlich, Bernhard (ed.) et al., Automated reasoning. 6th international joint conference, IJCAR 2012, Manchester, UK, June 26–29, 2012. Proceedings. Berlin: Springer (ISBN 978-3-642-31364-6/pbk). Lecture Notes in Computer Science 7364. Lecture Notes in Artificial Intelligence, 179-193 (2012).
Summary: 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.
For the entire collection see [Zbl 1245.68010].

68Q60 Specification and verification (program logics, model checking, etc.)
03B44 Temporal logic
68Q17 Computational difficulty of problems (lower bounds, completeness, difficulty of approximation, etc.)
68Q45 Formal languages and automata
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