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Consensus Game Acceptors

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Developments in Language Theory (DLT 2015)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 9168))

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Abstract

We study a game for recognising formal languages, in which two players with imperfect information need to coordinate on a common decision, given private input strings correlated by a finite graph. The players have a joint objective to avoid an inadmissible decision, in spite of the uncertainty induced by the input.

We show that the acceptor model based on consensus games characterises context-sensitive languages, and conversely, that winning strategies in such games can be described by context-sensitive languages. We also discuss consensus game acceptors with a restricted observation pattern that describe nondeterministic linear-time languages.

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References

  1. Alur, R., Henzinger, T.A., Kupferman, O.: Alternating-time temporal logic. J. ACM 49, 672–713 (2002)

    Article  MathSciNet  Google Scholar 

  2. Arnold, A., Walukiewicz, I.: Nondeterministic controllers of nondeterministic processes. In: Logic and Automata, vol. 2. Amsterdam University Press (2007)

    Google Scholar 

  3. Azhar, S., Peterson, G., Reif, J.: Lower bounds for multiplayer non-cooperative games of incomplete information. Journal of Computers and Mathematics with Applications 41, 957–992 (2001)

    Article  MathSciNet  Google Scholar 

  4. Berwanger, D., Kaiser, Ł.: Information tracking in games on graphs. Journal of Logic, Language and Information 19, 395–412 (2010)

    Article  MathSciNet  Google Scholar 

  5. Book, R.V., Greibach, S.A.: Quasi-realtime languages. Mathematical Systems Theory 4, 97–111 (1970)

    Article  MathSciNet  Google Scholar 

  6. Chandra, A.K., Kozen, D., Stockmeyer, L.J.: Alternation. Journal of the ACM 28, 114–133 (1981)

    Article  MathSciNet  Google Scholar 

  7. Chlebus, B.S.: Domino-tiling games. Journal of Computer and System Sciences 32, 374–392 (1986)

    Article  MathSciNet  Google Scholar 

  8. Chomsky, N., Schützenberger, M.: The algebraic theory of context-free languages. In: Computer Programming and Formal Systems. Studies in Logic and the Foundations of Mathematics, vol. 35, pp. 118–161. Elsevier (1963)

    Google Scholar 

  9. Fagin, R., Halpern, J.Y., Moses, Y., Vardi, M.Y.: Reasoning about Knowledge. MIT Press (1995)

    Google Scholar 

  10. Hearn, R.A., Demaine, E.D.: Games, Puzzles, and Computation. A. K. Peters Ltd., Natick (2009)

    Google Scholar 

  11. Janin, D.: On the (high) undecidability of distributed synthesis problems. In: van Leeuwen, J., Italiano, G.F., van der Hoek, W., Meinel, C., Sack, H., Plášil, F. (eds.) SOFSEM 2007. LNCS, vol. 4362, pp. 320–329. Springer, Heidelberg (2007)

    Chapter  Google Scholar 

  12. Kuroda, S.-Y.: Classes of languages and linear-bounded automata. Information and Control 7, 207–223 (1964)

    Article  MathSciNet  Google Scholar 

  13. Latteux, M., Simplot, D.: Context-sensitive string languages and recognizable picture languages. Information and Computation 138, 160–169 (1997)

    Article  MathSciNet  Google Scholar 

  14. Latteux, M., Simplot, D.: Recognizable picture languages and domino tiling. Theoretical Computer Science 178, 275–283 (1997)

    Article  MathSciNet  Google Scholar 

  15. Latteux, M., Simplot, D., Terlutte, A.: Iterated length-preserving rational transductions. In: Brim, L., Gruska, J., Zlatuška, J. (eds.) MFCS 1998. LNCS, vol. 1450, pp. 286–295. Springer, Heidelberg (1998)

    Chapter  Google Scholar 

  16. Mohalik, S., Walukiewicz, I.: Distributed games. In: Pandya, P.K., Radhakrishnan, J. (eds.) FSTTCS 2003. LNCS, vol. 2914, pp. 338–351. Springer, Heidelberg (2003)

    Chapter  Google Scholar 

  17. Okhotin, A.: Non-erasing variants of the Chomsky–Schützenberger theorem. In: Yen, H.-C., Ibarra, O.H. (eds.) DLT 2012. LNCS, vol. 7410, pp. 121–129. Springer, Heidelberg (2012)

    Chapter  Google Scholar 

  18. Peterson, G.L., Reif, J.H.: Multiple-person alternation. In: Proc. 20th Annual Symposium on Foundations of Computer Science (FOCS 1979), pp. 348–363. IEEE (1979)

    Google Scholar 

  19. Pnueli, A., Rosner, R.: Distributed reactive systems are hard to synthesize. In: Proceedings of the 31st Annual Symposium on Foundations of Computer Science, FoCS 1990, pp. 746–757. IEEE Computer Society Press (1990)

    Google Scholar 

  20. Sakarovitch, J.: Elements of Automata Theory. Cambridge University Press (2009)

    Google Scholar 

  21. Salomaa, A.: Formal Languages. Academic Press, New York (1973)

    Google Scholar 

  22. Schewe, S.: Distributed synthesis is simply undecidable. Inf. Process. Lett. 114, 203–207 (2014)

    Article  MathSciNet  Google Scholar 

  23. van Emde Boas, P.: The convenience of tilings. In: Complexity, Logic, and Recursion Theory. Lecture Notes in Pure and Applied Mathematics, vol. 18, pp. 331–363. Marcel Dekker Inc. (1997)

    Google Scholar 

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Author information

Authors and Affiliations

  1. LSV, ENS Cachan, CNRS and University of Paris-Saclay, Paris-Saclay, France

    Dietmar Berwanger & Marie van den Bogaard

Authors
  1. Dietmar Berwanger
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  2. Marie van den Bogaard
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Corresponding authors

Correspondence to Dietmar Berwanger or Marie van den Bogaard .

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Editors and Affiliations

  1. University of Liverpool, Liverpool, United Kingdom

    Igor Potapov

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Berwanger, D., van den Bogaard, M. (2015). Consensus Game Acceptors. In: Potapov, I. (eds) Developments in Language Theory. DLT 2015. Lecture Notes in Computer Science(), vol 9168. Springer, Cham. https://doi.org/10.1007/978-3-319-21500-6_8

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  • DOI: https://doi.org/10.1007/978-3-319-21500-6_8

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-21499-3

  • Online ISBN: 978-3-319-21500-6

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