Article

Free access

A combinatorial problem which is complete in polynomial space

Authors:

Shimon Even,

R. Endre TarjanAuthors Info & Claims

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

Pages 66 - 71

https://doi.org/10.1145/800116.803754

Published: 05 May 1975 Publication History

PDF eReader

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

[1]

S. Chase, "An implemented graph algorithm for winning Shannon switching games," IBM Research Technical Report RC-3121, Yorktown Heights, New York (1970).

Google Scholar

[2]

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

Digital Library

Google Scholar

[3]

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.

Google Scholar

[4]

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

Digital Library

Google Scholar

[5]

N. Nilsson, Problem-Solving Methods in Artificial Intelligence, McGraw-Hill, New York (1971).

Digital Library

Google Scholar

[6]

R. Tarjan, unpublished notes (1974).

Google Scholar

[7]

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

Digital Library

Google Scholar

Cited By

View all

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
Show More Cited By

Index Terms

A combinatorial problem which is complete in polynomial space

Recommendations

A Combinatorial Problem Which Is Complete in Polynomial Space

This paper considers a generalization, called the Shannon switching game on vertices, of a familiar board game called Hex. It is shown that determining who wins such a game if each player plays perfectly is very hard; in fact, if this game problem is ...
Solving 7×7 Hex with domination, fill-in, and virtual connections
Advances in computer games

We present an algorithm that determines the outcome of an arbitrary Hex game-state by finding a winning virtual connection for the winning player. Our algorithm recursively searches the game-tree, combining fixed and dynamic game-state virtual ...
How to play Reverse Hex

We present new results on how to play Reverse Hex, also known as Rex, or Misère Hex, on n í n boards. We give new proofs-and strengthened versions-of Lagarias and Sleator's theorem (for n í n boards, each player can prolong the game until the board is ...

Comments

Please enable JavaScript to view thecomments powered by Disqus.

Information & Contributors

Information

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]

Publisher

Association for Computing Machinery

New York, NY, United States

Publication History

Published: 05 May 1975

Permissions

Request permissions for this article.

Request Permissions

Check for updates

Author Tags

Qualifiers

Article

Acceptance Rates

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

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

Upcoming Conference

STOC '25

Sponsor:
sigact

57th Annual ACM Symposium on Theory of Computing (STOC 2025)

June 23 - 27, 2025

Prague , Czech Republic

Contributors

Other Metrics

View Article Metrics

Bibliometrics & Citations

Bibliometrics

Article Metrics

15
Total Citations
View Citations
114
Total Downloads

Downloads (Last 12 months)29
Downloads (Last 6 weeks)2

Reflects downloads up to 21 Dec 2024

Other Metrics

View Author Metrics

Citations

Cited By

View all

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
https://dl.acm.org/doi/10.1145/800135.804422
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
Show More Cited By

View Options

View options

PDF

View or Download as a PDF file.

PDF

eReader

View online with eReader.

eReader

Login options

Check if you have access through your login credentials or your institution to get full access on this article.

Cited By

Index Terms

Recommendations

A Combinatorial Problem Which Is Complete in Polynomial Space

Solving 7×7 Hex with domination, fill-in, and virtual connections

How to play Reverse Hex