GO Is Polynomial-Space Hard

@article{Lichtenstein1980GOIP,
  title={GO Is Polynomial-Space Hard},
  author={David Lichtenstein and Michael Sipser},
  journal={J. ACM},
  year={1980},
  volume={27},
  pages={393-401}
}
It is shown that, given an arbitrary GO position on an n × n board, the problem of determining the winner is Pspace hard. New techniques are exploited to overcome the difficulties arising from the planar nature of board games. In particular, it is proved that GO is Pspace hard by reducing a Pspace-complete set, TQBF, to a game called generalized geography, then to a planar version of that game, and finally to GO. 
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References

SHOWING 1-10 OF 10 REFERENCES
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. Expand
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. Expand
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. Expand
On the Complexity of Some Two-Person Perfect-Information Games
  • T. Schaefer
  • Computer Science, Mathematics
  • J. Comput. Syst. Sci.
  • 1978
Abstract We present a number of two-person games, based on simple combinatorial ideas, for which the problem of deciding whether the first player can win is complete in polynomial space. ThisExpand
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. Expand
Electronics Res Lab
  • Electronics Res Lab
  • 1978
Axioms for GO SIGART Newsletter (ACM), 51 (April 1975), p 13 3 CHANDRA, A K, AND STOC~EYER
  • L J Alternation 17th Annual IEEE Syrup Found Comptr Scl,
  • 1973
To appear 2 BLOCK, H C Axioms for GO SIGART
  • Alternation 17th Annual IEEE Syrup Found Comptr Scl
  • 1973
requmng exponential time Preliminary Report Proc 5th Annual ACM Symp Theory Comptg
  • requmng exponential time Preliminary Report Proc 5th Annual ACM Symp Theory Comptg
  • 1973