Benedikt Bollig ; Karin Quaas ; Arnaud Sangnier - The Complexity of Flat Freeze LTL

lmcs:4657 - Logical Methods in Computer Science, September 30, 2019, Volume 15, Issue 3 -
The Complexity of Flat Freeze LTLArticle

Authors: Benedikt Bollig ; Karin Quaas ; Arnaud Sangnier

    We consider the model-checking problem for freeze LTL on one-counter automata (OCA). 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. In a previous work, Lechner et al. showed that model checking for flat freeze LTL on OCA 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 OCA with parameterized tests (OCA(P)). The new aspect is that we simulate OCA(P) 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 OCA(P) with unary updates. We obtain our main result as a corollary. As another application, relying on a reduction by Bundala and Ouaknine, one obtains an alternative proof of the known fact that reachability in closed parametric timed automata with one parametric clock is in NEXPTIME.

    Volume: Volume 15, Issue 3
    Published on: September 30, 2019
    Accepted on: August 19, 2019
    Submitted on: July 3, 2018
    Keywords: Computer Science - Formal Languages and Automata Theory,Computer Science - Logic in Computer Science


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