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In the game of Go, the question of whether a ladder—a method of capturing stones—works, is shown to be PSPACE-complete. Our reduction closely follows that of Lichtenstein and Sipser [LS80], who first showed PSPACE-hardness of Go by letting the outcome of a game depend on the capture of a large group of stones. We achieve greater simplicity by avoiding the… (More)

For two-player games of perfect information such as Checker, Chess, Go, etc., we introduce " uniqueness " properties. For any game position, we say roughly that it has a uniqueness property (or, a unique solution property) if a winning strategy (if it exists) is forced to be unique. Depending on the way that winning strategy is forced, a uniqueness property… (More)

We devise an efficient protocol by which a series of two-person games Gi with unique winning strategies can be combined into a single game G with unique winning strategy, even when the result of G is a non-monotone function of the results of the Gi that is unknown to the players. In computational complexity terms, we show that the class UAP of Niedermeier… (More)

For two-player games of perfect information such as Checkers, Chess, and Go we introduce " uniqueness " properties. A game position has a uniqueness property if a winning strategy—should one exist—is forced to be unique. Depending on the way that winning strategy is forced, a uniqueness property is classified as weak , strong, or global. We prove that any… (More)

SUMMARY We show that a problem of deciding whether a formula for a multivariate polynomial of n variables over a finite field of characteristic 2 has degree n when reduced modulo a certain Boolean ideal belongs to P. When the formula is allowed to have succinct representations as sums of monomials, the problem becomes P-complete. key words: degree of… (More)

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