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Taming past LTL and flat counter systems
, 2012
"... Abstract. Reachability and LTL modelchecking 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 ..."
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Abstract. Reachability and LTL modelchecking 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 NPcomplete 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 quantifierfree Presburger formulae. Other complexity results are proved, for instance for restricted classes of flat counter systems. 1
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"... Abstract. Explicitstate model checkers like SPIN, which verify systems against properties stated in lineartime temporal logic (LTL), rely on efficient LTLtoBüchi translators. A difficult design decision in such constructions is to trade time spent on minimizing the Büchi automaton versus tim ..."
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Abstract. Explicitstate model checkers like SPIN, which verify systems against properties stated in lineartime temporal logic (LTL), rely on efficient LTLtoBüchi translators. A difficult design decision in such constructions is to trade time spent on minimizing the Büchi automaton versus time spent on model checking against an unnecessarily large automaton. Standard reduction methods like simulation quotienting are fast but often miss optimization opportunities. We propose a new technique that achieves significant further reductions when more time can be invested in the minimization of the automaton. The additional effort is often justified, for example, when the properties are known in advance, or when the same property is used in multiple model checking runs. We use a modified SAT solver to perform bounded language inclusion checks on partial solutions. SAT solving allows us to prune large parts of the search space for smaller automata already in the early solving stages. The bound allows us to finetune the algorithm to run in limited time. Our experimental results show that, on standard LTLtoBüchi benchmarks, our prototype implementation achieves a significant further size reduction on automata obtained by the best currently available LTLtoBüchi translators. 1