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DOI: 10.4230/LIPIcs.TIME.2020.14

One-Pass Context-Based Tableaux Systems for CTL and ECTL

Authors: Alex Abuin, Alexander Bolotov, Montserrat Hermo, and Paqui Lucio

Published in: LIPIcs, Volume 178, 27th International Symposium on Temporal Representation and Reasoning (TIME 2020)

Abstract

When building tableau for temporal logic formulae, applying a two-pass construction, we first check the validity of the given tableaux input by creating a tableau graph, and then, in the second "pass", we check if all the eventualities are satisfied. In one-pass tableaux checking the validity of the input does not require these auxiliary constructions. This paper continues the development of one-pass tableau method for temporal logics introducing tree-style one-pass tableau systems for Computation Tree Logic (CTL) and shows how this can be extended to capture Extended CTL (ECTL). A distinctive feature here is the utilisation, for the core tableau construction, of the concept of a context of an eventuality which forces its earliest fulfilment. Relevant algorithms for obtaining a systematic tableau for these branching-time logics are also defined. We prove the soundness and completeness of the method. With these developments of a tree-shaped one-pass tableau for CTL and ECTL, we have formalisms which are well suited for the automation and are amenable for the implementation, and for the formulation of dual sequent calculi. This brings us one step closer to the application of one-pass context-based tableaux in certified model checking for a variety of CTL-type branching-time logics.

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Alex Abuin, Alexander Bolotov, Montserrat Hermo, and Paqui Lucio. One-Pass Context-Based Tableaux Systems for CTL and ECTL. In 27th International Symposium on Temporal Representation and Reasoning (TIME 2020). Leibniz International Proceedings in Informatics (LIPIcs), Volume 178, pp. 14:1-14:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2020)

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@InProceedings{abuin_et_al:LIPIcs.TIME.2020.14,
  author =	{Abuin, Alex and Bolotov, Alexander and Hermo, Montserrat and Lucio, Paqui},
  title =	{{One-Pass Context-Based Tableaux Systems for CTL and ECTL}},
  booktitle =	{27th International Symposium on Temporal Representation and Reasoning (TIME 2020)},
  pages =	{14:1--14:20},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-167-2},
  ISSN =	{1868-8969},
  year =	{2020},
  volume =	{178},
  editor =	{Mu\~{n}oz-Velasco, Emilio and Ozaki, Ana and Theobald, Martin},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.TIME.2020.14},
  URN =		{urn:nbn:de:0030-drops-129824},
  doi =		{10.4230/LIPIcs.TIME.2020.14},
  annote =	{Keywords: Temporal logic, fairness, expressiveness, branching-time}
}

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DOI: 10.4230/LIPIcs.TIME.2019.12

Towards Certified Model Checking for PLTL Using One-Pass Tableaux

Authors: Alex Abuin, Alexander Bolotov, Unai Díaz de Cerio, Montserrat Hermo, and Paqui Lucio

Published in: LIPIcs, Volume 147, 26th International Symposium on Temporal Representation and Reasoning (TIME 2019)

Abstract

The standard model checking setup analyses whether the given system specification satisfies a dedicated temporal property of the system, providing a positive answer here or a counter-example. At the same time, it is often useful to have an explicit proof that certifies the satisfiability. This is exactly what the certified model checking (CMC) has been introduced for. The paper argues that one-pass (context-based) tableau for PLTL can be efficiently used in the CMC setting, emphasising the following two advantages of this technique. First, the use of the context in which the eventualities occur, forces them to fulfil as soon as possible. Second, a dual to the tableau sequent calculus can be used to formalise the certificates. The combination of the one-pass tableau and the dual sequent calculus enables us to provide not only counter-examples for unsatisfied properties, but also proofs for satisfied properties that can be checked in a proof assistant. In addition, the construction of the tableau is enriched by an embedded solver, to which we dedicate those (propositional) computational tasks that are costly for the tableaux rules applied solely. The combination of the above techniques is particularly helpful to reason about large (system) specifications.

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Alex Abuin, Alexander Bolotov, Unai Díaz de Cerio, Montserrat Hermo, and Paqui Lucio. Towards Certified Model Checking for PLTL Using One-Pass Tableaux. In 26th International Symposium on Temporal Representation and Reasoning (TIME 2019). Leibniz International Proceedings in Informatics (LIPIcs), Volume 147, pp. 12:1-12:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2019)

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@InProceedings{abuin_et_al:LIPIcs.TIME.2019.12,
  author =	{Abuin, Alex and Bolotov, Alexander and D{\'\i}az de Cerio, Unai and Hermo, Montserrat and Lucio, Paqui},
  title =	{{Towards Certified Model Checking for PLTL Using One-Pass Tableaux}},
  booktitle =	{26th International Symposium on Temporal Representation and Reasoning (TIME 2019)},
  pages =	{12:1--12:18},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-127-6},
  ISSN =	{1868-8969},
  year =	{2019},
  volume =	{147},
  editor =	{Gamper, Johann and Pinchinat, Sophie and Sciavicco, Guido},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.TIME.2019.12},
  URN =		{urn:nbn:de:0030-drops-113702},
  doi =		{10.4230/LIPIcs.TIME.2019.12},
  annote =	{Keywords: Temporal logic, fairness, expressiveness, linear-time, Certified model checking}
}

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Documents authored by Abuin, Alex

One-Pass Context-Based Tableaux Systems for CTL and ECTL

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Towards Certified Model Checking for PLTL Using One-Pass Tableaux

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