On the Complexity of Tsume-Go

“…Crâşmaru and Tromp [CT00] show that it is PSPACE-complete to determine whether a ladder (a repeated pattern of capture threats) results in a capture. Finally, Crâşmaru [Crâ99] shows that it is NP-complete to determine the status of certain restricted forms of life-and-death problems in Go.…”

Section: Gomentioning

confidence: 99%

Playing games with algorithms: Algorithmic combinatorial game theory

Demaine¹,

Hearn²

2009

Games of No Chance 3

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Combinatorial games lead to several interesting, clean problems in algorithms and complexity theory, many of which remain open. The purpose of this paper is to provide an overview of the area to encourage further research. In particular, we begin with general background in Combinatorial Game Theory, which analyzes ideal play in perfect-information games, and Constraint Logic, which provides a framework for showing hardness. Then we survey results about the complexity of determining ideal play in these games, and the related problems of solving puzzles, in terms of both polynomial-time algorithms and computational intractability results. Our review of background and survey of algorithmic results are by no means complete, but should serve as a useful primer.

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“…As a matter of fact, Go has very simple rules, is very difficult for computers, is central in education in many Asian countries (part of school activities in some countries) and has NP-completeness properties for some families of situations [12], and PSPACE-hardness for others [21], and EXPTIMEcompleteness for some versions [23]. It has also been chosen as a testbed for artificial intelligence by many researchers.…”

Section: Methodsmentioning

confidence: 99%