N by N Checkers is Exptime Complete
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History
Submitted: 25 August 1981
Published online: 13 July 2006
Publication Data
ISSN (print): 0097-5397
ISSN (online): 1095-7111
CODEN: smjcat
DOI:10.1137/0213018
The game of Checkers can easily be generalized to be played on an N by N board and the complexity of deciding questions about positions regarded as a function of N. This paper considers mainly the question of whether a particular player can force a win from a given position and also the question of what is the best move in a given position. Each of these problems is shown to be complete in exponential time. This means that any algorithm to solve them must take time which rises exponentially with respect to some power of N and moreover that they are amongst the hardest problems with such a time bound.For instance if there are any problems solvable in exponential time but not in polynomial space, then these two problems are amongst them.
Copyright © 1984 Society for Industrial and Applied Mathematics
Permalink: http://dx.doi.org/10.1137/0213018
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