Journal of Logic, Language and Information

, Volume 19, Issue 4, pp 395–412 | Cite as

Information Tracking in Games on Graphs



When seeking to coordinate in a game with imperfect information, it is often relevant for a player to know what other players know. Keeping track of the information acquired in a play of infinite duration may, however, lead to infinite hierarchies of higher-order knowledge. We present a construction that makes explicit which higher-order knowledge is relevant in a game and allows us to describe a class of games that admit coordinated winning strategies with finite memory.


Infinite games Imperfect information Distributed strategies Multiplayer games 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. Arnold, A., & Walukiewicz, I. (2007). Nondeterministic controllers of nondeterministic processes. In Logic and automata (Vol. 2). Amsterdam University Press.Google Scholar
  2. Berwanger, D. (2010). Infinite coordination games. In Logic and the foundations of game and decision theory (LOFT9), texts in logic and games. Amsterdam University Press, To appear.Google Scholar
  3. Chandra A. K., Kozen D., Stockmeyer L. J. (1981) Alternation. Journal of ACM 28: 114–133CrossRefGoogle Scholar
  4. Chatterjee, K., Doyen, L., Henzinger, T. A., & Raskin, J.-F. (2006). Algorithms for omega-regular games with imperfect information. In Proceedings of the 20th International Workshop on Computer Science Logic (CSL), 15th Annual Conference of the EACSL, Vol. 4207 of LNCS (pp. 287–302). Springer.Google Scholar
  5. Gale D., Stewart F. M. (1953) Infinite games with perfect information. Annals of Mathematics Studies 28: 245–266Google Scholar
  6. Gastin P., Sznajder N., Zeitoun M. (2009) Distributed synthesis for well-connected architectures. Formal Methods in System Design 34: 215–237CrossRefGoogle Scholar
  7. Henzinger, T. A. (2005) Games in system design and verification. In Proceedings of the 10th Conference on Theoretical Aspects of Rationality and Knowledge (TARK-2005).Google Scholar
  8. Kupferman, O., & Vardi, M. Y. (2001). Synthesizing distributed systems, In Proceedings of the 16th Annual IEEE Symposium on Logic in Computer Science.Google Scholar
  9. McNaughton R. (1993) Infinite games played on finite graphs. Annals of Pure and Applied Logic 65: 149–184CrossRefGoogle Scholar
  10. Peterson, G. L., & Reif, J. H. (1979). Multiple-Person alternation. In Proceedings of the 20th Annual Symposium on Foundations of Computer Science, (FOCS 1979), IEEE (pp. 348–363).Google Scholar
  11. Pnueli, A., & Rosner, E. (1989). On the synthesis of a reactive module. In Proceedings of the 16th ACM SIGPLAN-SIGACT symposium on Principles of programming languages (pp. 179–190). ACM Press.Google Scholar
  12. Ramadge P. J., Wonham W. M. (1987) Supervisory control of a class of discrete event processes. SIAM Journal Control and Optimization 25: 206–230CrossRefGoogle Scholar
  13. Reif J. (1984) The complexity of two-player games of incomplete information. Journal of Computer and System Sciences 29: 274–301CrossRefGoogle Scholar
  14. Rudie, K., & Wonham, W. M. (1990). Supervisory control of communicating processes. In L. Logrippo, R. L. Probert, & H. Ural (Eds.), Proceedings of PSTV 1990, Tenth International Symposium on Protocol Specification, Testing and Verification (pp. 243–257). North-Holland.Google Scholar
  15. Rudie K., Wonham W. M. (1992) Think globally, act locally: Decentralized supervisory control. IEEE Transactions on Automatic Control 37: 1692–1708CrossRefGoogle Scholar
  16. Thomas, W. (1995). On the synthesis of strategies in infinite games. In STACS 95, Proceedings of the Symposium on Theoretical Aspects of Computer Science (pp. 1–13).Google Scholar
  17. Tripakis S. (2004) Undecidable problems of decentralized observation and control on regular languages. Information Processing Letters 90: 21–28CrossRefGoogle Scholar
  18. Walukiewicz, I. (2004). A landscape with games in the background. In Proceedings of the 15th Annual IEEE Symposium on Logic in Computer Science (LICS 2004) (pp. 356–366).Google Scholar

Copyright information

© Springer Science+Business Media B.V. 2010

Authors and Affiliations

  1. 1.LSV, CNRS & ENS CachanParisFrance
  2. 2.RWTHAachenGermany

Personalised recommendations