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Model Checking Resource Bounded Systems with Shared Resources via Alternating Büchi Pushdown Systems

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PRIMA 2015: Principles and Practice of Multi-Agent Systems (PRIMA 2015)

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 9387))

Abstract

It is well known that the verification of resource-constrained multi-agent systems is undecidable in general. In many such settings, resources are private to agents. In this paper, we investigate the model checking problem for a resource logic based on Alternating-Time Temporal Logic (ATL) with shared resources. Resources can be consumed and produced up to any amount. We show that the model checking problem is undecidable if two or more of such unbounded resources are available. Our main technical result is that in the case of a single shared resource, the problem becomes decidable. Although intuitive, the proof of decidability is non-trivial. We reduce model checking to a problem over alternating Büchi pushdown systems. An intermediate result connects to general automata-based verification: we show that model checking Computation Tree Logic (CTL) over (compact) alternating Büchi pushdown systems is decidable.

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References

  1. Alechina, N., Logan, B., Nguyen, H.N., Raimondi, F.: Decidable model-checking for a resource logic with production of resources. In: Proceedings of the 21st European Conference on Artificial Intelligence (ECAI-2014), pp. 9–14. ECCAI. IOS Press (2014)

    Google Scholar 

  2. Alechina, N., Logan, B., Nguyen, H.N., Rakib, A.: Resource-bounded alternating-time temporal logic. In: Proceedings of the 9th International Conference on Autonomous Agents and Multiagent Systems (AAMAS 2010), pp. 481–488. IFAAMAS (2010)

    Google Scholar 

  3. Alechina, N., Bulling, N., Logan, B., Nguyen, H.N.: On the boundary of (un)decidability: decidable model-checking for a fragment of resource agent logic. In: Proceedings of the Twenty-Fourth International Joint Conference on Artificial Intelligence, IJCAI 2015, Buenos Aires, Argentina, 25–31 July 2015, pp. 1494–1501 (2015)

    Google Scholar 

  4. Alur, R., Henzinger, T., Kupferman, O.: Alternating-time temporal logic. Journal of the ACM 49(5), 672–713 (2002)

    Article  MathSciNet  MATH  Google Scholar 

  5. Bouajjani, A., Esparza, J., Maler, O.: Reachability analysis of pushdown automata: application to model-checking. In: Mazurkiewicz, A., Winkowski, J. (eds.) CONCUR 1997. LNCS, vol. 1243, pp. 135–150. Springer, Heidelberg (1997)

    Chapter  Google Scholar 

  6. Bozzelli, L.: Complexity results on branching-time pushdown model checking. Theoretical Computer Science 379(1), 286–297 (2007)

    Article  MathSciNet  MATH  Google Scholar 

  7. Bulling, N., Farwer, B.: Expressing properties of resource-bounded systems: the logics \({\sf {RTL}}^{*}\) and \({\sf {RTL}}\). In: Dix, J., Fisher, M., Novák, P. (eds.) CLIMA X. LNCS, vol. 6214, pp. 22–45. Springer, Heidelberg (2010)

    Chapter  Google Scholar 

  8. Bulling, N., Farwer, B.: On the (un-)decidability of model checking resource-bounded agents. In: Proceedings of the 19th European Conference on Artificial Intelligence (ECAI 2010), vol. 215, pp. 567–572. IOS Press (2010)

    Google Scholar 

  9. Bulling, N., Nguyen, H.N.: Model checking resource bounded systems with shared resources via alternating Büchi pushdown systems. Technical report. ArXiv e-prints (2015)

    Google Scholar 

  10. Cachat, T.: Symbolic strategy synthesis for games on pushdown graphs. In: Widmayer, P., Triguero, F., Morales, R., Hennessy, M., Eidenbenz, S., Conejo, R. (eds.) ICALP 2002. LNCS, vol. 2380, p. 704. Springer, Heidelberg (2002)

    Chapter  Google Scholar 

  11. Clarke, E., Grumberg, O., Peled, D.: Model Checking. MIT Press (1999)

    Google Scholar 

  12. Clarke, E.M., Emerson, E.A.: Design and synthesis of synchronization skeletons using branching time temporal logic. In: Kozen, D. (ed.) Logics of Programs. LNCS, vol. 131, pp. 52–71. Springer, Heidelberg (1981)

    Chapter  Google Scholar 

  13. Della Monica, D., Napoli, M., Parente, M.: Model checking coalitional games in shortage resource scenarios. In: Proceedings of the 4th International Symposium on Games, Automata, Logics and Formal Verification (GandALF 2013). EPTCS, vol. 119, pp. 240–255 (2013)

    Google Scholar 

  14. Hopcroft, J.E., Ullman, J.D.: Introduction to Automata Theory, Languages, and Computation. Addison-Wesley (1979)

    Google Scholar 

  15. Song, F., Touili, T.: Efficient CTL model-checking for pushdown systems. Theoretical Computer Science 549, 127–145 (2014)

    Article  MathSciNet  MATH  Google Scholar 

  16. Suwimonteerabuth, D., Schwoon, S., Esparza, J.: Efficient algorithms for alternating pushdown systems with an application to the computation of certificate chains. In: Graf, S., Zhang, W. (eds.) ATVA 2006. LNCS, vol. 4218, pp. 141–153. Springer, Heidelberg (2006)

    Chapter  Google Scholar 

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Author information

Authors and Affiliations

  1. Delft University of Technology, Delft, The Netherlands

    Nils Bulling

  2. School of Computer Science, University of Nottingham, Nottingham, UK

    Hoang Nga Nguyen

Authors
  1. Nils Bulling
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  2. Hoang Nga Nguyen
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Corresponding authors

Correspondence to Nils Bulling or Hoang Nga Nguyen .

Editor information

Editors and Affiliations

  1. Jinan University, Guangzhou, China

    Qingliang Chen

  2. Università di Bologna, Bologna, Italy

    Paolo Torroni

  3. Inria - Sophia Antipolis-Méditerran, Sophia Antipolis, France

    Serena Villata

  4. National Taiwan University, Taipei, Taiwan

    Jane Hsu

  5. Università di Bologna, Bologna, Italy

    Andrea Omicini

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Bulling, N., Nguyen, H.N. (2015). Model Checking Resource Bounded Systems with Shared Resources via Alternating Büchi Pushdown Systems. In: Chen, Q., Torroni, P., Villata, S., Hsu, J., Omicini, A. (eds) PRIMA 2015: Principles and Practice of Multi-Agent Systems. PRIMA 2015. Lecture Notes in Computer Science(), vol 9387. Springer, Cham. https://doi.org/10.1007/978-3-319-25524-8_47

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  • DOI: https://doi.org/10.1007/978-3-319-25524-8_47

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-25523-1

  • Online ISBN: 978-3-319-25524-8

  • eBook Packages: Computer ScienceComputer Science (R0)

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