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How Much Lookahead is Needed to Win Infinite Games?

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Automata, Languages, and Programming (ICALP 2015)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 9135))

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Abstract

Delay games are two-player games of infinite duration in which one player may delay her moves to obtain a lookahead on her opponent’s moves. For \(\omega \)-regular winning conditions it is known that such games can be solved in doubly-exponential time and that doubly-exponential lookahead is sufficient.

We improve upon both results by giving an exponential time algorithm and an exponential upper bound on the necessary lookahead. This is complemented by showing \(\textsc {ExpTime}\)-hardness of the solution problem and tight exponential lower bounds on the lookahead. Both lower bounds already hold for safety conditions. Furthermore, solving delay games with reachability conditions is shown to be \(\textsc {PSpace}\)-complete.

Partially supported by the DFG projects “TriCS” (ZI 1516/1-1) and “AVACS” (SFB/TR 14). The first author was supported by an IMPRS-CS PhD Scholarship.

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References

  1. Büchi, J.R., Landweber, L.H.: Solving sequential conditions by finite-state strategies. Trans. Amer. Math. Soc. 138, 295–311 (1969)

    Article  MATH  MathSciNet  Google Scholar 

  2. Carayol, A., Löding, C.: MSO on the infinite binary tree: choice and order. In: Duparc, J., Henzinger, T.A. (eds.) CSL 2007. LNCS, vol. 4646, pp. 161–176. Springer, Heidelberg (2007)

    Chapter  Google Scholar 

  3. Carayol, A., Löding, C.: Uniformization in automata theory. In: Schroeder-Heister, P., Heinzmann, G., Hodges, W., Bour, P.E. (eds.) CLMPS. College Publications, London (2012) (to appear)

    Google Scholar 

  4. Chandra, A.K., Kozen, D., Stockmeyer, L.J.: Alternation. J. ACM 28(1), 114–133 (1981)

    Article  MATH  MathSciNet  Google Scholar 

  5. Fridman, W., Löding, C., Zimmermann, M.: Degrees of lookahead in context-free infinite games. In: Bezem, M. (ed.) CSL 2011. LIPIcs, vol. 12, pp. 264–276. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2011)

    Google Scholar 

  6. Gurevich, Y., Shelah, S.: Rabin’s uniformization problem. The Journal of Symbolic Logic 48, 1105–1119 (1983)

    Article  MATH  MathSciNet  Google Scholar 

  7. Holtmann, M., Kaiser, L., Thomas, W.: Degrees of lookahead in regular infinite games. LMCS 8(3) (2012)

    Google Scholar 

  8. Hosch, F.A., Landweber, L.H.: Finite delay solutions for sequential conditions. In: ICALP 1972, pp. 45–60 (1972)

    Google Scholar 

  9. Hutagalung, M., Lange, M., Lozes, É.: Buffered simulation games for Büchi automata. In: Ésik, Z., Fülöp, Z. (eds.) AFL 2014. EPTCS, vol. 151, pp. 286–300 (2014)

    Google Scholar 

  10. Klein, F., Zimmermann, M.: How much lookahead is needed to win infinite games? (2014). arXiv: 1412.3701

  11. Klein, F., Zimmermann, M.: What are strategies in delay games? Borel determinacy for games with lookahead (2015). arXiv: 1504.02627

  12. Löding, C., Winter, S.: Synthesis of deterministic top-down tree transducers from automatic tree relations. In: Peron, A., Piazza, C. (eds.) GandALF 2014. EPTCS, vol. 161, pp. 88–101 (2014)

    Google Scholar 

  13. Schewe, S.: Solving parity games in big steps. In: Arvind, V., Prasad, S. (eds.) FSTTCS 2007. LNCS, vol. 4855, pp. 449–460. Springer, Heidelberg (2007)

    Chapter  Google Scholar 

  14. Thomas, W., Lescow, H.: Logical specifications of infinite computations. In: de Bakker, J.W., de Roever, W.-P., Rozenberg, G. (eds.) REX 1993. LNCS, vol. 803, pp. 583–621. Springer, Heidelberg (1994)

    Chapter  Google Scholar 

  15. Trakhtenbrot, B., Barzdin, I.: Finite Automata; Behavior and Synthesis. Fundamental Studies in Computer Science, vol. 1. North-Holland Publishing Company, New York. American Elsevier (1973)

    Google Scholar 

  16. Zimmermann, M.: Delay games with WMSO+U winning conditions. In: CSR 2015 (2015, to appear). arXiv: 1412.3978

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Authors and Affiliations

  1. Reactive Systems Group, Saarland University, Saarbrücken, Germany

    Felix Klein & Martin Zimmermann

Authors
  1. Felix Klein
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  2. Martin Zimmermann
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Correspondence to Felix Klein .

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Editors and Affiliations

  1. Reykjavik University, Reykjavik, Iceland

    Magnús M. Halldórsson

  2. Kyoto University, Kyoto, Japan

    Kazuo Iwama

  3. The University of Tokyo, Tokyo, Japan

    Naoki Kobayashi

  4. Technische Universiteit Eindhoven, Eindhoven, The Netherlands

    Bettina Speckmann

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Klein, F., Zimmermann, M. (2015). How Much Lookahead is Needed to Win Infinite Games?. In: Halldórsson, M., Iwama, K., Kobayashi, N., Speckmann, B. (eds) Automata, Languages, and Programming. ICALP 2015. Lecture Notes in Computer Science(), vol 9135. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-47666-6_36

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  • DOI: https://doi.org/10.1007/978-3-662-47666-6_36

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-662-47665-9

  • Online ISBN: 978-3-662-47666-6

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