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Alternating-Time Temporal Logic in the Calculus of (Co)Inductive Constructions

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Abstract

This work presents a complete formalization of Alternating-time Temporal Logic (ATL) and its semantic model, Concurrent Game Structures (CGS), in the Calculus of (Co)Inductive Constructions, using the logical framework Coq. Unlike standard ATL semantics, temporal operators are formalized in terms of inductive and coinductive types, employing a fixpoint characterization of these operators. The formalization is used to model a concurrent system with an unbounded number of players and states, and to verify some properties expressed as ATL formulas. Unlike automatic techniques, our formal model has no restrictions in the size of the CGS, and arbitrary state predicates can be used as atomic propositions of ATL.

Keywords

  • Move Vector
  • Temporal Logic
  • Linear Temporal Logic
  • Atomic Proposition
  • Liveness Property

These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References

  1. Alur, R., Henzinger, T.A., Kupferman, O.: Alternating-Time Temporal Logic. In: de Roever, W.-P., Langmaack, H., Pnueli, A. (eds.) COMPOS 1997. LNCS, vol. 1536, pp. 23–60. Springer, Heidelberg (1998)

    CrossRef  Google Scholar 

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

    MathSciNet  CrossRef  Google Scholar 

  3. Alur, R., Henzinger, T., Mang, F., Qadeer, S., Rajamani, S., Tasiran, S.: Mocha: Modularity in Model Checking. In: Vardi, M.Y. (ed.) CAV 1998. LNCS, vol. 1427, pp. 521–525. Springer, Heidelberg (1998)

    CrossRef  Google Scholar 

  4. Bertot, Y., Castéran, P.: Interactive Theorem Proving and Program Development. Coq’Art: The Calculus of Inductive Constructions. In: Texts in Theoretical Computer Science. Springer (2004)

    Google Scholar 

  5. Chadha, R., Kremer, S., Scedrov, A.: Formal analysis of multiparty contract signing. Journal of Automated Reasoning 36(1-2), 39–83 (2006)

    MathSciNet  MATH  CrossRef  Google Scholar 

  6. Coquand, T., Huet, G.: The Calculus of Constructions. In: Information and Computation, vol. 76, pp. 95–120. Academic Press (February/March 1988)

    Google Scholar 

  7. Coupet-Grimal, S.: LTL in Coq. Contributions to the Coq system, Laboratoire d’Informatique Fondamentale de Marseille (2002), http://coq.inria.fr/contribs/LTL.tar.gz

  8. Emerson, E.: Temporal and modal logic. In: Handbook of Theoretical Computer Science, pp. 995–1072. Elsevier (1995)

    Google Scholar 

  9. Giménez, E.: A Calculus of Infinite Constructions and its application to the verification of communicating systems. PhD thesis, Ecole Normale Supérieure de Lyon (1996)

    Google Scholar 

  10. Goranko, V., van Drimmelen, G.: Complete axiomatization and decidability of alternating-time temporal logic. Theoretical Computer Science 353(1), 93–117 (2006)

    MathSciNet  MATH  CrossRef  Google Scholar 

  11. Kremer, S., Raskin, J.: A game-based verification of non-repudiation and fair exchange protocols. Journal of Computer Security 11(3), 399–429 (2003)

    Google Scholar 

  12. Leroy, X.: Formal verification of a realistic compiler. Communications of the ACM 52(7), 107–115 (2009)

    CrossRef  Google Scholar 

  13. Luna, C.: Computation tree logic for reactive systems and timed computation tree logic for real time systems. Contributions to the Coq system, Universidad de la República, Uruguay (2000)

    Google Scholar 

  14. Merz, S.: An encoding of TLA in Isabelle. Technical report, Institut für Informatic, Universität München, Germany (1999)

    Google Scholar 

  15. Paulin-Mohring, C.: Inductive Definitions in the System Coq - rules and Properties. In: Bezem, M., Groote, J.F. (eds.) TLCA 1993. LNCS, vol. 664, pp. 328–345. Springer, Heidelberg (1993)

    CrossRef  Google Scholar 

  16. Pnueli, A.: The temporal logic of programs. In: Proceedings of the 18th Annual Symposium on Foundations of Computer Science, pp. 46–57. IEEE Computer Society, Washington, DC (1977)

    Google Scholar 

  17. Pnueli, A., Arons, T.: tlpvs: A pvs-Based ltl Verification System. In: Dershowitz, N. (ed.) Verification: Theory and Practice. LNCS, vol. 2772, pp. 598–625. Springer, Heidelberg (2004)

    Google Scholar 

  18. Schneider, K., Hoffmann, D.W.: A HOL Conversion for Translating Linear Time Temporal Logic to ω-Automata. In: Bertot, Y., Dowek, G., Hirschowitz, A., Paulin, C., Théry, L. (eds.) TPHOLs 1999. LNCS, vol. 1690, pp. 255–272. Springer, Heidelberg (1999)

    CrossRef  Google Scholar 

  19. The Coq development team. The Coq proof assistant reference manual, version 8.2. LogiCal Project, Distributed electronically (2010), http://coq.inria.fr

  20. The Coq development team. The Coq Standard Library. LogiCal Project (2010), http://coq.inria.fr/stdlib/

  21. van Leeuwen, J. (ed.): Handbook of Theoretical Computer Science, vol. B: Formal Models and Semantics. Elsevier and MIT Press (1990)

    Google Scholar 

  22. Zanarini, D.: Formalización de lógica temporal alternante en el cálculo de construcciones coinductivas. Master’s thesis, FCEIA, Universidad Nacional de Rosario, Argentina (2008), http://www.fceia.unr.edu.ar/~dante

  23. Zanarini, D.: Formalization of alternating time temporal logic in Coq (2010), http://www.fceia.unr.edu.ar/~dante

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Zanarini, D., Luna, C., Sierra, L. (2012). Alternating-Time Temporal Logic in the Calculus of (Co)Inductive Constructions. In: Gheyi, R., Naumann, D. (eds) Formal Methods: Foundations and Applications. SBMF 2012. Lecture Notes in Computer Science, vol 7498. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-33296-8_16

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  • DOI: https://doi.org/10.1007/978-3-642-33296-8_16

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-33295-1

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