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A combinatorial problem which is complete in polynomial space

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Shimon Even and

R. Endre TarjanAuthors Info & Claims

STOC '75: Proceedings of the seventh annual ACM symposium on Theory of computing

May 1975

Pages 66 - 71

https://doi.org/10.1145/800116.803754

Published: 05 May 1975 Publication History

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Abstract

We consider a generalization, which we call the Shannon switching game on vertices, of a familiar board game called HEX. We show that determining who wins such a game if each player plays perfectly is very hard; in fact, it is as hard as carrying out any polynomial-space-bounded computation. This result suggests that the theory of combinatorial games is difficult.

References

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S. Cook, "The complexity of theorem-proving procedures," Proceedings Third Annual ACM Symposium on Theory of Computing (1971), 151-158.

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R. Karp, "Reducibility among combinatorial problems," Complexity of Computer Computations, R.E. Miller and J.W. Thatcher, eds., Plenum Press, New York (1972), 85-104.

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A.R. Meyer and L.J. Stockmeyer, "Words problems requiring exponential time," Proceedings Fifth Annual ACM Symposium on Theory of Computing (1973), 1-9.

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R. Tarjan, unpublished notes (1974).

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R. Tarjan, "Depth-first search and linear graph algorithms," SIAM J. Comput., Vol. 1, No. 2 (1972), 146-160.

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Cited By

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Nguyen VPerrot K(2022)Rikudo is NP-completeTheoretical Computer Science10.1016/j.tcs.2022.01.034Online publication date: Jan-2022
https://doi.org/10.1016/j.tcs.2022.01.034
Nguyen VPerrot KVallet M(2020) -completeness of the game Kingdomino Theoretical Computer Science10.1016/j.tcs.2020.04.007822(23-35)Online publication date: Jun-2020
https://doi.org/10.1016/j.tcs.2020.04.007
Slany W(2002)Endgame problems of Sim-like graph Ramsey avoidance games are PSPACE-completeTheoretical Computer Science10.1016/S0304-3975(01)00179-7289:1(829-843)Online publication date: 23-Oct-2002
https://dl.acm.org/doi/10.1016/S0304-3975%2801%2900179-7
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A combinatorial problem which is complete in polynomial space

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Published In

STOC '75: Proceedings of the seventh annual ACM symposium on Theory of computing

May 1975

265 pages

ISBN:9781450374194

DOI:10.1145/800116

Permission to make digital or hard copies of all or part of this work for personal or classroom use is granted without fee provided that copies are not made or distributed for profit or commercial advantage and that copies bear this notice and the full citation on the first page. Copyrights for components of this work owned by others than ACM must be honored. Abstracting with credit is permitted. To copy otherwise, or republish, to post on servers or to redistribute to lists, requires prior specific permission and/or a fee. Request permissions from [email protected]

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Association for Computing Machinery

New York, NY, United States

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Published: 05 May 1975

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STOC '75 Paper Acceptance Rate 31 of 87 submissions, 36%;

Overall Acceptance Rate 1,469 of 4,586 submissions, 32%

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Cited By

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Nguyen VPerrot K(2022)Rikudo is NP-completeTheoretical Computer Science10.1016/j.tcs.2022.01.034Online publication date: Jan-2022
https://doi.org/10.1016/j.tcs.2022.01.034
Nguyen VPerrot KVallet M(2020) -completeness of the game Kingdomino Theoretical Computer Science10.1016/j.tcs.2020.04.007822(23-35)Online publication date: Jun-2020
https://doi.org/10.1016/j.tcs.2020.04.007
Slany W(2002)Endgame problems of Sim-like graph Ramsey avoidance games are PSPACE-completeTheoretical Computer Science10.1016/S0304-3975(01)00179-7289:1(829-843)Online publication date: 23-Oct-2002
https://dl.acm.org/doi/10.1016/S0304-3975%2801%2900179-7
Yamasaki Y(1993)Shannon-like games are difficultDiscrete Mathematics10.5555/2784051.2784336111:1(481-483)Online publication date: 22-Feb-1993
https://dl.acm.org/doi/10.5555/2784051.2784336
Reisch S(1981)Hex ist PSPACE-vollständigActa Informatica10.1007/BF0028896415:2(167-191)Online publication date: 1-Jun-1981
https://dl.acm.org/doi/10.1007/BF00288964
Fraenkel A(1980)From Nim to GoCombinatorial Mathematics, Optimal Designs and Their Applications10.1016/S0167-5060(08)70700-3(137-156)Online publication date: 1980
https://doi.org/10.1016/S0167-5060(08)70700-3
Reisch S(1980)Gobang ist PSPACE-vollständigActa Informatica10.1007/BF0028853613:1(59-66)Online publication date: 1-Jan-1980
https://dl.acm.org/doi/10.1007/BF00288536
Reif JFischer MDemillo RLynch NBurkhard WAho A(1979)Universal games of incomplete informationProceedings of the eleventh annual ACM symposium on Theory of computing10.1145/800135.804422(288-308)Online publication date: 30-Apr-1979
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Sakoda WSipser MLipton RBurkhard WSavitch WFriedman EAho A(1978)Nondeterminism and the size of two way finite automataProceedings of the tenth annual ACM symposium on Theory of computing10.1145/800133.804357(275-286)Online publication date: 1-May-1978
https://dl.acm.org/doi/10.1145/800133.804357
Schaefer TChandra AWotschke DFriedman EHarrison M(1976)Complexity of decision problems based on finite two-person perfect-information gamesProceedings of the eighth annual ACM symposium on Theory of computing10.1145/800113.803629(41-49)Online publication date: 3-May-1976
https://dl.acm.org/doi/10.1145/800113.803629
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