Acta Informatica

, Volume 13, Issue 1, pp 59–66

Gobang ist PSPACE-vollständig

  • Stefan Reisch
Article

Gobang is PSPACE-complete

Summary

For many games, the decision problem of whether a player in a given situation has a winning strategy has been shown to be PSPACE-complete. Following the PSPACE-completeness results of Even and Tarjan [1] for generalized Hex on graphs and of Schaefer [6] for a variety of combinatorial games, the decision problems were shown to be PSPACE-hard for generalizations of Go and Checkers. In this paper a corresponding theorem is proved for the board-game Gobang, a variant of Go. Since the decision problem for Gobang states-of-play itself lies in PSPACE, it can be shown that Gobang is in fact PSPACE-complete.

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Literatur

  1. 1.
    Even, S., Tarjan, R.E.: A combinatorial problem which is complete in polynomial space. 7-th Annual ACM Symposium on Theory of Computing 1975, pp. 66–71Google Scholar
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    Fraenkel, A.S., Garey, M.R., Johnson, D.S., Schaefer, T.J., Yesha, Y.: The complexity of checkers on an n × n Board. 19-th Annual Symposium on Foundations of Computer-Science, 1978, pp. 55–64Google Scholar
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    Lichtenstein, D., Sipser, M.: Go is PSPACE-hard. 19-th Annual Symposium on Foundations of Computer-Science, 1978, pp. 48–54Google Scholar
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    Meyer, A.R., Stockmeyer, L.J.: Word problems requiring exponential time. Proceedings of the 5-th Annual ACM Symposium on Theory of Computing, 1973, pp. 1–9Google Scholar
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    Paul, W.J.: Komplexitätstheorie. Stuttgart: Teubner 1978Google Scholar
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    Schaefer, T.J.: On the complexity of some two-person-perfect-information games. Comput. System Sci. 16, 185–225 (1978)Google Scholar

Copyright information

© Springer-Verlag 1980

Authors and Affiliations

  • Stefan Reisch
    • 1
  1. 1.Fakultät für MathematikUniversität BielefeldBielefeld 1Bundesrepublik Deutschland

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