منابع مشابه
Winning Positions in Simplicial Nim
Simplicial Nim, introduced by Ehrenborg and Steingŕımsson, is a generalization of the classical two-player game of Nim. The heaps are placed on the vertices of a simplicial complex and a player’s move may affect any number of piles provided that the corresponding vertices form a face of the complex. In this paper, we present properties of a complex that are equivalent to the P-positions (winnin...
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An evolutionary approach for computing the winning strategy for Nim-like games is proposed in this paper. The winning strategy is computed by using the Multi Expression Programming (MEP) technique a fast and efficient variant of the Genetic Programming (GP). Each play strategy is represented by a mathematical expression that contains mathematical operators (such as +, -, *, mod, div, and , or, ...
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We introduce a generalization of the classical game of Nim by placing the piles on the vertices of a simplicial complex and allowing a move to affect the piles on any set of vertices that forms a face of the complex. Under certain conditions on the complex we present a winning strategy. These conditions are satisfied, for instance, when the simplicial complex consists of the independent sets of...
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In this paper we will fully characterize all types of winning moves in the “takeaway” game of Fibonacci Nim. We prove the known winning algorithm as a corollary of the general winning algorithm and then show that no other winning algorithms exist. As a by-product of our investigation of the game, we will develop useful properties of Fibonacci numbers. We conclude with an exploration of the prob...
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We consider infinite two-player games on pushdown graphs. For parity winning conditions, we show that the set of winning positions of each player is regular and we give an effective construction of an alternating automaton recognizing it. This provides a DEXPTIME procedure to decide whether a position is winning for a given player. Finally, using the same methods, we show, for any ω-regular win...
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ژورنال
عنوان ژورنال: The Electronic Journal of Combinatorics
سال: 2010
ISSN: 1077-8926
DOI: 10.37236/356