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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-dev.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}
}

Document

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-dev.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}
}

Document

DOI: 10.4230/LIPIcs.TIME.2018.5

Extending Fairness Expressibility of ECTL+: A Tree-Style One-Pass Tableau Approach

Authors: Alexander Bolotov, Montserrat Hermo, and Paqui Lucio

Published in: LIPIcs, Volume 120, 25th International Symposium on Temporal Representation and Reasoning (TIME 2018)

Abstract

Temporal logic has become essential for various areas in computer science, most notably for the specification and verification of hardware and software systems. For the specification purposes rich temporal languages are required that, in particular, can express fairness constraints. For linear-time logics which deal with fairness in the linear-time setting, one-pass and two-pass tableau methods have been developed. In the repository of the CTL-type branching-time setting, the well-known logics ECTL and ECTL^+ were developed to explicitly deal with fairness. However, due to the syntactical restrictions, these logics can only express restricted versions of fairness. The logic CTL^*, often considered as "the full branching-time logic" overcomes these restrictions on expressing fairness. However, this logic itself, is extremely challenging for the application of verification techniques, and the tableau technique, in particular. For example, there is no one-pass tableau construction for this logic, while it is known that one-pass tableau has an additional benefit enabling the formulation of dual sequent calculi that are often treated as more "natural" being more friendly for human understanding. Based on these two considerations, the following problem arises - are there logics that have richer expressiveness than ECTL^+ yet "simpler" than CTL^* for which a one-pass tableau can be developed? In this paper we give a solution to this problem. We present a tree-style one-pass tableau for a sub-logic of CTL^* that we call ECTL^#, which is more expressive than ECTL^+ allowing the formulation of a new range of fairness constraints with "until" operator. The presentation of the tableau construction is accompanied by an algorithm for constructing a systematic tableau, for any given input of admissible branching-time formulae. We prove the termination, soundness and completeness of the method. As tree-shaped one-pass tableaux are well suited for the automation and are amenable for the implementation and for the formulation of sequent calculi, our results also open a prospect of relevant developments of the automation and implementation of the tableau method for ECTL^#, and of a dual sequent calculi.

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Alexander Bolotov, Montserrat Hermo, and Paqui Lucio. Extending Fairness Expressibility of ECTL+: A Tree-Style One-Pass Tableau Approach. In 25th International Symposium on Temporal Representation and Reasoning (TIME 2018). Leibniz International Proceedings in Informatics (LIPIcs), Volume 120, pp. 5:1-5:22, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2018)

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@InProceedings{bolotov_et_al:LIPIcs.TIME.2018.5,
  author =	{Bolotov, Alexander and Hermo, Montserrat and Lucio, Paqui},
  title =	{{Extending Fairness Expressibility of ECTL+: A Tree-Style One-Pass Tableau Approach}},
  booktitle =	{25th International Symposium on Temporal Representation and Reasoning (TIME 2018)},
  pages =	{5:1--5:22},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-089-7},
  ISSN =	{1868-8969},
  year =	{2018},
  volume =	{120},
  editor =	{Alechina, Natasha and N{\o}rv\r{a}g, Kjetil and Penczek, Wojciech},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.TIME.2018.5},
  URN =		{urn:nbn:de:0030-drops-97704},
  doi =		{10.4230/LIPIcs.TIME.2018.5},
  annote =	{Keywords: Temporal logic, fairness, tableau, branching-time, one-pass tableau}
}

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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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Extending Fairness Expressibility of ECTL+: A Tree-Style One-Pass Tableau Approach

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