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Deciding Monotonic Games

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Computer Science Logic (CSL 2003)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 2803))

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Abstract

In an earlier work [AČJYK00] we presented a general framework for verification of infinite-state transition systems, where the transition relation is monotonic with respect to a well quasi-ordering on the set of states. In this paper, we investigate extending the framework from the context of transition systems to that of games. We show that monotonic games are in general undecidable. We identify a subclass of monotonic games, called downward closed games. We provide algorithms for analyzing downward closed games subject to winning conditions which are formulated as safety properties.

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References

  1. Abdulla, P.A., Čerāns, K., Jonsson, B., Yih-Kuen, T.: Algorithmic analysis of programs with well quasi-ordered domains. Information and Computation 160, 109–127 (2000)

    Article  MATH  MathSciNet  Google Scholar 

  2. Alur, R., Dill, D.: Automata for modelling real-time systems. In: Paterson, M. (ed.) ICALP 1990. LNCS, vol. 443, pp. 322–335. Springer, Heidelberg (1990)

    Chapter  Google Scholar 

  3. Alur, R., Henzinger, T., Kupferman, O.: Alternating-time temporal logic. In: Proc. 38th Annual Symp. Foundations of Computer Science, pp. 100–109 (1997)

    Google Scholar 

  4. Abdulla, P.A., Jonsson, B.: Undecidable verification problems for programs with unreliable channels. Information and Computation 130(1), 71–90 (1996)

    Article  MATH  MathSciNet  Google Scholar 

  5. Abdulla, P.A., Jonsson, B.: Verifying programs with unreliable channels. Information and Computation 127(2), 91–101 (1996)

    Article  MATH  MathSciNet  Google Scholar 

  6. Abdulla, P.A., Nylén, A.: Timed Petri nets and BQOs. In: Colom, J.-M., Koutny, M. (eds.) ICATPN 2001. LNCS, vol. 2075, pp. 53–70. Springer, Heidelberg (2001)

    Chapter  Google Scholar 

  7. Barzdin, J.M., Bicevskis, J.J., Kalninsh, A.A.: Automatic construction of complete sample systems for program testing. In: IFIP Congress 1977 (1977)

    Google Scholar 

  8. Bouajjani, A., Mayr, R.: Model checking lossy vector addition systems. In: Meinel, C., Tison, S. (eds.) STACS 1999. LNCS, vol. 1563, pp. 323–333. Springer, Heidelberg (1999)

    Chapter  Google Scholar 

  9. Čerāns, K.: Deciding properties of integral relational automata. In: Shamir, E., Abiteboul, S. (eds.) ICALP 1994. LNCS, vol. 820, pp. 35–46. Springer, Heidelberg (1994)

    Google Scholar 

  10. de Alfaro, L.: How to specify and verify the long-run average behavior of probabilistic systems. In: Proc. LICS 1998 13th IEEE Int. Symp. on Logic in Computer Science (1998)

    Google Scholar 

  11. de Alfaro, L., Henzinger, T., Majumdar, R.: Symbolic algorithms for infinite state games. In: Larsen, K.G., Nielsen, M. (eds.) CONCUR 2001. LNCS, vol. 2154, p. 536. Springer, Heidelberg (2001)

    Chapter  Google Scholar 

  12. Delzanno, G.: Automatic verification of cache coherence protocols. In: Emerson, E.A., Sistla, A.P. (eds.) CAV 2000. LNCS, vol. 1855, pp. 53–68. Springer, Heidelberg (2000)

    Chapter  Google Scholar 

  13. Delzanno, G., Esparza, J., Podelski, A.: Constraint-based analysis of broadcast protocols. In: Flum, J., Rodríguez-Artalejo, M. (eds.) CSL 1999. LNCS, vol. 1683, pp. 50–66. Springer, Heidelberg (1999)

    Chapter  Google Scholar 

  14. Esparza, J., Finkel, A., Mayr, R.: On the verification of broadcast protocols. In: Proc. LICS 1999 14th IEEE Int. Symp. on Logic in Computer Science (1999)

    Google Scholar 

  15. Finkel, A.: Decidability of the termination problem for completely specified protocols. Distributed Computing 7(3) (1994)

    Google Scholar 

  16. Finkel, A., Schnoebelen, P.: Well-structured transition systems everywhere. Technical Report LSV-98-4, Ecole Normale Supérieure de Cachan (April 1998)

    Google Scholar 

  17. Higman, G.: Ordering by divisibility in abstract algebras. Proc. London Math. Soc. 2, 326–336 (1952)

    Article  MATH  MathSciNet  Google Scholar 

  18. Mayr, R.: Undecidable problems in unreliable computations. In: Gonnet, G.H., Viola, A. (eds.) LATIN 2000. LNCS, vol. 1776, Springer, Heidelberg (2000)

    Chapter  Google Scholar 

  19. Thomas, W.: Infinite games and verification. In: Brinksma, E., Larsen, K.G. (eds.) CAV 2002. LNCS, vol. 2404, pp. 58–64. Springer, Heidelberg (2002)

    Chapter  Google Scholar 

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Author information

Authors and Affiliations

  1. Uppsala University, Sweden

    Parosh Aziz Abdulla & Julien d’Orso

  2. University of Paris 7, France

    Ahmed Bouajjani

Authors
  1. Parosh Aziz Abdulla
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  2. Ahmed Bouajjani
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  3. Julien d’Orso
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Editor information

Editors and Affiliations

  1. Institute of Discrete Mathematics and Geometry, Technical University Vienna, Wiedner Hauptstrasse 8-10, A-1040, Wien, Austria

    Matthias Baaz

  2. Members of EACSL Jury for the Ackermann Award,  

    Johann A. Makowsky

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Abdulla, P.A., Bouajjani, A., d’Orso, J. (2003). Deciding Monotonic Games. In: Baaz, M., Makowsky, J.A. (eds) Computer Science Logic. CSL 2003. Lecture Notes in Computer Science, vol 2803. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-45220-1_1

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  • DOI: https://doi.org/10.1007/978-3-540-45220-1_1

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-40801-7

  • Online ISBN: 978-3-540-45220-1

  • eBook Packages: Springer Book Archive

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