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International Conference on Formal Engineering Methods

ICFEM 2017: Formal Methods and Software Engineering pp 36–53Cite as

Model Checking Pushdown Epistemic Game Structures

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Part of the book series: Lecture Notes in Computer Science ((LNPSE,volume 10610))

Abstract

In this paper, we investigate the problem of verifying pushdown multi-agent systems with imperfect information. As the formal model, we introduce pushdown epistemic game structures (PEGSs), an extension of pushdown game structures with epistemic accessibility relations (EARs). For the specification, we consider extensions of alternating-time temporal logics with epistemic modalities: ATEL, ATEL\(^*\) and AEMC. We study the model checking problems for ATEL, ATEL\(^*\) and AEMC over PEGSs under various imperfect information settings. For ATEL and ATEL\(^*\), we show that size-preserving EARs, a common definition of the accessibility relation in the literature of games over pushdown systems with imperfect information, will render the model checking problem undecidable under imperfect information and imperfect recall setting. We then propose regular EARs, and provide automata-theoretic model checking algorithms with matching low bounds, i.e., EXPTIME-complete for ATEL and 2EXPTIME-complete for ATEL\(^*\). In contrast, for AEMC, we show that the model checking problem is EXPTIME-complete even in the presence of size-preserving EARs.

This work was partially supported by NSFC grant (61402179, 61532019, 61662035, 61572478, 61472474, 61100062, and 61272135), UK EPSRC grant (EP/P00430X/1), and European CHIST-ERA project SUCCESS.

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Notes

  1. 1.

    One may notice that, in the definition of PEGSs, \(\varDelta \) is defined as a complete function \(P\times \varGamma \times \mathcal {D}\rightarrow P\times \varGamma ^*\), meaning that all actions are available to each agent. This does not restrict the expressiveness of PEGSs, as we can easily add transitions to some additional sink state to simulate the situation where some actions are unavailable to some agents.

  2. 2.

    “complete” means that \(\varDelta (q, \gamma )\) is defined for each \((q,\gamma ) \in Q \times \varGamma \).

  3. 3.

    Since normal PEGS only pops one symbol from the stack at one step, in order to pop m symbols, we need to introduce some additional control states as done in [30].

  4. 4.

    \(\langle {\emptyset }\rangle \) (resp. \([{\emptyset }]\)) is the universal (resp. existential) path quantification A (resp. E).

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Author information

Authors and Affiliations

  1. Department of Computer Science and Information Systems, Birkbeck, University of London, London, UK

    Taolue Chen

  2. School of Information Science and Technology, ShanghaiTech University, Shanghai, China

    Fu Song

  3. State Key Laboratory of Computer Science, Institute of Software, Chinese Academy of Sciences, Beijing, China

    Zhilin Wu

  4. State Key Laboratory of Novel Software Technology, Nanjing University, Nanjing, China

    Taolue Chen

Authors
  1. Taolue Chen
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  2. Fu Song
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  3. Zhilin Wu
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Correspondence to Fu Song .

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Editors and Affiliations

  1. Xidian University, Xi’an, China

    Zhenhua Duan

  2. University of Oxford, Oxford, United Kingdom

    Luke Ong

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Chen, T., Song, F., Wu, Z. (2017). Model Checking Pushdown Epistemic Game Structures. In: Duan, Z., Ong, L. (eds) Formal Methods and Software Engineering. ICFEM 2017. Lecture Notes in Computer Science(), vol 10610. Springer, Cham. https://doi.org/10.1007/978-3-319-68690-5_3

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  • DOI: https://doi.org/10.1007/978-3-319-68690-5_3

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