The Complexity of Flat Freeze LTL

Authors Benedikt Bollig, Karin Quaas, Arnaud Sangnier

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Benedikt Bollig
Karin Quaas
Arnaud Sangnier

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Benedikt Bollig, Karin Quaas, and Arnaud Sangnier. The Complexity of Flat Freeze LTL. In 28th International Conference on Concurrency Theory (CONCUR 2017). Leibniz International Proceedings in Informatics (LIPIcs), Volume 85, pp. 33:1-33:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2017)


We consider the model-checking problem for freeze LTL on one-counter automata (OCAs). Freeze LTL extends LTL with the freeze quantifier, which allows one to store different counter values of a run in registers so that they can be compared with one another. As the model-checking problem is undecidable in general, we focus on the flat fragment of freeze LTL, in which the usage of the freeze quantifier is restricted. Recently, Lechner et al. showed that model checking for flat freeze LTL on OCAs with binary encoding of counter updates is decidable and in 2NEXPTIME. In this paper, we prove that the problem is, in fact, NEXPTIME-complete no matter whether counter updates are encoded in unary or binary. Like Lechner et al., we rely on a reduction to the reachability problem in OCAs with parameterized tests (OCAPs). The new aspect is that we simulate OCAPs by alternating two-way automata over words. This implies an exponential upper bound on the parameter values that we exploit towards an NP algorithm for reachability in OCAPs with unary updates. We obtain our main result as a corollary.
  • one-counter automata
  • freeze LTL
  • model checking


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