Advertisement

Exploring the Boundary of Half Positionality

  • Alessandro Bianco
  • Marco Faella
  • Fabio Mogavero
  • Aniello Murano
Part of the Lecture Notes in Computer Science book series (LNCS, volume 6245)

Abstract

Half positionality is the property of a language of infinite words to admit positional winning strategies, when interpreted as the goal of a two-player game on a graph. Such problem applies to the automatic synthesis of controllers, where positional strategies represent efficient controllers. As our main result, we describe a novel sufficient condition for half positionality, more general than what was previously known. Moreover, we compare our proposed condition with several others, proposed in the recent literature, outlining an intricate network of relationships, where only few combinations are sufficient for half positionality.

Keywords

Regular Language Winning Strategy Tree Automaton Positional Strategy Strong Monotonicity 
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.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. [Cac02]
    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, pp. 704–715. Springer, Heidelberg (2002)CrossRefGoogle Scholar
  2. [CN06]
    Colcombet, T., Niwinski, D.: On the positional determinacy of edge-labeled games. Theor. Comput. Sci. 352(1-3), 190–196 (2006)zbMATHCrossRefMathSciNetGoogle Scholar
  3. [EJ91]
    Emerson, E.A., Jutla, C.S.: Tree automata, mu-calculus and determinacy. In: FOCS 1991, pp. 368–377. IEEE Computer Society Press, Los Alamitos (1991)Google Scholar
  4. [Gra04]
    Gradel, E.: Positional determinancy of infinite games. In: Diekert, V., Habib, M. (eds.) STACS 2004. LNCS, vol. 2996, pp. 4–18. Springer, Heidelberg (2004)Google Scholar
  5. [GZ05]
    Gimbert, H., Zielonka, W.: Games where you can play optimally without any memory. In: Abadi, M., de Alfaro, L. (eds.) CONCUR 2005. LNCS, vol. 3653, pp. 428–442. Springer, Heidelberg (2005)CrossRefGoogle Scholar
  6. [Kop06]
    Kopczyński, E.: Half-positional determinancy of infinite games. In: Bugliesi, M., Preneel, B., Sassone, V., Wegener, I. (eds.) ICALP 2006. LNCS, vol. 4052, pp. 336–347. Springer, Heidelberg (2006)CrossRefGoogle Scholar
  7. [Kop07]
    Kopczyński, E.: Omega-regular half-positional winning conditions. In: Duparc, J., Henzinger, T.A. (eds.) CSL 2007. LNCS, vol. 4646, pp. 41–53. Springer, Heidelberg (2007)CrossRefGoogle Scholar
  8. [KVW01]
    Kupferman, O., Vardi, M.Y., Wolper, P.: Module checking. Information and Computation 164, 322–344 (2001)zbMATHCrossRefMathSciNetGoogle Scholar
  9. [McN93]
    McNaughton, R.: Infinite games played on finite graphs. Annals of Pure and Applied Logic 65, 149–184 (1993)zbMATHCrossRefMathSciNetGoogle Scholar
  10. [Mos91]
    Mostowski, A.W.: Games with forbidden positions. Technical Report 78, Uniwersytet Gdański, Instytut Matematyki (1991)Google Scholar
  11. [Tho95]
    Thomas, W.: On the synthesis of strategies in infinite games. In: Mayr, E.W., Puech, C. (eds.) STACS 1995. LNCS, vol. 900, pp. 1–13. Springer, Heidelberg (1995)Google Scholar
  12. [Zie98]
    Zielonka, W.: Infinite games on finitely coloured graphs with applications to automata on infinite trees. J. of Theor. Comp. Sci. 200(1-2), 135–183 (1998)zbMATHCrossRefMathSciNetGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2010

Authors and Affiliations

  • Alessandro Bianco
    • 1
  • Marco Faella
    • 1
  • Fabio Mogavero
    • 1
  • Aniello Murano
    • 1
  1. 1.Università degli Studi di Napoli ”Federico II”Italy

Personalised recommendations