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DOI: 10.4230/LIPIcs.CONCUR.2016.29

Model Checking Flat Freeze LTL on One-Counter Automata

Authors: Antonia Lechner, Richard Mayr, Joël Ouaknine, Amaury Pouly, and James Worrell

Published in: LIPIcs, Volume 59, 27th International Conference on Concurrency Theory (CONCUR 2016)

Abstract

Freeze LTL is a temporal logic with registers that is suitable for specifying properties of data words. In this paper we study the model checking problem for Freeze LTL on one-counter automata. This problem is known to be undecidable in full generality and PSPACE-complete for the special case of deterministic one-counter automata. Several years ago, Demri and Sangnier investigated the model checking problem for the flat fragment of Freeze LTL on several classes of counter automata and posed the decidability of model checking flat Freeze LTL on one-counter automata as an open problem. In this paper we resolve this problem positively, utilising a known reduction to a reachability problem on one-counter automata with parameterised equality and disequality tests. Our main technical contribution is to show decidability of the latter problem by translation to Presburger arithmetic.

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Antonia Lechner, Richard Mayr, Joël Ouaknine, Amaury Pouly, and James Worrell. Model Checking Flat Freeze LTL on One-Counter Automata. In 27th International Conference on Concurrency Theory (CONCUR 2016). Leibniz International Proceedings in Informatics (LIPIcs), Volume 59, pp. 29:1-29:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2016)

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@InProceedings{lechner_et_al:LIPIcs.CONCUR.2016.29,
  author =	{Lechner, Antonia and Mayr, Richard and Ouaknine, Jo\"{e}l and Pouly, Amaury and Worrell, James},
  title =	{{Model Checking Flat Freeze LTL on One-Counter Automata}},
  booktitle =	{27th International Conference on Concurrency Theory (CONCUR 2016)},
  pages =	{29:1--29:14},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-017-0},
  ISSN =	{1868-8969},
  year =	{2016},
  volume =	{59},
  editor =	{Desharnais, Jos\'{e}e and Jagadeesan, Radha},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.CONCUR.2016.29},
  URN =		{urn:nbn:de:0030-drops-61841},
  doi =		{10.4230/LIPIcs.CONCUR.2016.29},
  annote =	{Keywords: one-counter automata, disequality tests, reachability, freeze LTL, Presburger arithmetic}
}

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Model Checking Flat Freeze LTL on One-Counter Automata

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