Marcel Crâsmaru

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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)
We devise an efficient protocol by which a series of twoperson 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)
In this paper, we explain why Go is hard to be programmed. Since the strategy of the game is closely related to the concept of alive– dead group, it is plainly necessary to analyze this concept. For this a mathematical model is proposed. Then we turn our research to TsumeGo problems in which one of the players has always a unique good move and the other has(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)
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)
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