Gobang ist PSPACE-vollständig

SummaryFor 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.

[1]  David S. Johnson,et al.  The complexity of checkers on an N × N board , 1978, 19th Annual Symposium on Foundations of Computer Science (sfcs 1978).

[2]  Robert E. Tarjan,et al.  A combinatorial problem which is complete in polynomial space , 1975, STOC.

[3]  David Lichtenstein,et al.  GO is pspace hard , 1978, 19th Annual Symposium on Foundations of Computer Science (sfcs 1978).

[4]  Albert R. Meyer,et al.  Word problems requiring exponential time(Preliminary Report) , 1973, STOC.

[5]  Thomas J. Schaefer,et al.  On the Complexity of Some Two-Person Perfect-Information Games , 1978, J. Comput. Syst. Sci..