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Distributed Games and Distributed Control for Asynchronous Systems

  • Paul Gastin
  • Benjamin Lerman
  • Marc Zeitoun
Part of the Lecture Notes in Computer Science book series (LNCS, volume 2976)

Abstract

We introduce distributed games over asynchronous transition systems to model a distributed controller synthesis problem. A game involves two teams and is not turn-based: several players of both teams may simultaneously be enabled. We define distributed strategies based on the causal view that players have of the system. We reduce the problem of finding a winning distributed strategy with a given memory to finding a memoryless winning distributed strategy in a larger distributed game. We reduce the latter problem to finding a strategy in a classical 2-players game. This allows to transfer results from the sequential case to this distributed setting.

Keywords

Distributed game distributed control distributed strategy 

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References

  1. 1.
    Cori, R., Métivier, Y., Zielonka, W.: Asynchronous mappings and asynchronous cellular automata. Inform. and Comput. 106, 159–202 (1993)zbMATHCrossRefMathSciNetGoogle Scholar
  2. 2.
    Diekert, V., Métivier, Y.: Partial Commutations and Traces. In: Handbook of Formal languages, vol. 3, pp. 457–533. Springer, Heidelberg (1997)Google Scholar
  3. 3.
    Diekert, V., Rozenberg, G. (eds.): The Book of Traces. World Scientific, Singapore (1995)Google Scholar
  4. 4.
    Kupferman, O., Vardi, M.Y.: Synthesizing distributed systems. In: Proc. of the LICS 2001. Computer Society Press (2001)Google Scholar
  5. 5.
    Madhusudan, P., Thiagarajan, P.S.: Distributed controller synthesis for local specifications. In: Orejas, F., Spirakis, P.G., van Leeuwen, J. (eds.) ICALP 2001. LNCS, vol. 2076, pp. 396–407. Springer, Heidelberg (2001)CrossRefGoogle Scholar
  6. 6.
    Madhusudan, P., Thiagarajan, P.S.: A decidable class of asynchronous distributed controllers. In: Brim, L., Jančar, P., Křetínský, M., Kucera, A. (eds.) CONCUR 2002. LNCS, vol. 2421, pp. 145–160. Springer, Heidelberg (2002)CrossRefGoogle Scholar
  7. 7.
    Mohalik, S., Walukiewicz, I.: Distributed games. In: Pandya, P.K., Radhakrishnan, J. (eds.) FSTTCS 2003. LNCS, vol. 2914, pp. 338–351. Springer, Heidelberg (2003)CrossRefGoogle Scholar
  8. 8.
    Pin, J., Perrin, D.: Infinite words. Automata, Semigroups, Logic and Games. Elsevier, Amsterdam (to appear)Google Scholar
  9. 9.
    Pnueli, A., Rosner, R.: Distributed reactive systems are hard to synthetize. In: Proc. of the 31st IEEE Symp. FOCS, pp. 746–757 (1990)Google Scholar
  10. 10.
    Ramadge, P., Wonham, W.: The control of discrete event systems. Proceedings of the IEEE 77, 81–98 (1989)CrossRefGoogle Scholar
  11. 11.
    Thomas, W.: Infinite games and verification. In: Brinksma, E., Larsen, K.G. (eds.) CAV 2002. LNCS, vol. 2404, pp. 58–64. Springer, Heidelberg (2002)CrossRefGoogle Scholar
  12. 12.
    Vöge, J., Jurdziński, M.: A discrete strategy improvement algorithm for solving parity games. In: Emerson, E.A., Sistla, A.P. (eds.) CAV 2000. LNCS, vol. 1855, pp. 202–215. Springer, Heidelberg (2000)CrossRefGoogle Scholar
  13. 13.
    Zielonka, W.: Asynchronous automata. In: Rozenberg, G., Diekert, V. (eds.) Book of Traces, pp. 175–217. World Scientific, Singapore (1995)Google Scholar
  14. 14.
    Zielonka, W.: Infinite games on finitely coloured graphs with applications to automata on infinite trees. Theoretical Computer Science 200(1-2), 135–183 (1998)zbMATHCrossRefMathSciNetGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2004

Authors and Affiliations

  • Paul Gastin
    • 1
  • Benjamin Lerman
    • 1
  • Marc Zeitoun
    • 1
  1. 1.LIAFAUniversité Paris 7 & CNRSParis cedex 05France

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