Hex ist PSPACE-vollständig

@article{Reisch2004HexIP,
  title={Hex ist PSPACE-vollst{\"a}ndig},
  author={Stefan Reisch},
  journal={Acta Informatica},
  year={2004},
  volume={15},
  pages={167-191}
}
  • S. Reisch
  • Published 1 June 1981
  • Mathematics
  • Acta Informatica
SummaryThere are a number of board games such as Checkers [2], Go [5], and Gobang [8], which are known to be PSPACE-hard. This means that the problem to determine the player having a winning strategy in a given situation on an n×n board of one of these games is as hard to solve as everything computable in polynomial space. PSPACE-completeness has been previously proven for some combinatorial games played on graphs or by logical formulas [1, 9].In this paper we will show that the same holds for… 
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References

SHOWING 1-10 OF 10 REFERENCES
Gobang ist PSPACE-vollständig
TLDR
It can be shown that Gobang is in fact PSPACE-complete, a variant of Go, since the decision problem for Gobang states-of-play itself lies in PSPACE.
GO is pspace hard
TLDR
A great deal of effort has been spent in the search for optimal and computationally feasible game strategies, but recently it has become possible to provide compelling evidence that such strategies may not always exist.
The complexity of checkers on an N × N board
TLDR
Under certain reasonable assumptions about the "drawing rule" in force, the problem of whether a specified player can force a win against best play by his opponent is shown to be PSPACE-hard.
On the Complexity of Some Two-Person Perfect-Information Games
A Combinatorial Problem Which Is Complete in Polynomial Space
TLDR
It is shown that determining who wins such a game if each player plays perfectly is very hard; this result suggests that the theory of combinational games is difficult.
Word problems requiring exponential time(Preliminary Report)
TLDR
A number of similar decidable word problems from automata theory and logic whose inherent computational complexity can be precisely characterized in terms of time or space requirements on deterministic or nondeterministic Turing machines are considered.
Efficient Planarity Testing
TLDR
An efficient algorithm to determine whether an arbitrary graph G can be embedded in the plane is described, which used depth-first search and has time and space bounds.
Mathematische Rätsel und Probleme
Gobang is PSPACE-vollstS.ndig
  • Acta Informat
  • 1980
Word problems requiring exponential time
  • 5th annual ACM Symposium on Theory of Computing,
  • 1973