Poset Game Periodicity
نویسنده
چکیده
Poset games are two-player impartial combinatorial games, with normal play convention. Starting with any poset, the players take turns picking an element of the poset, and removing that and all larger elements from the poset. Examples of poset games include Chomp, Nim, Hackendot, Subset-Takeaway, and others. We prove a general theorem about poset games, which we call the Poset Game Perioidicity Theorem: as a poset expands along two chains, positions of the associated poset games with any fixed g-value have a regular, periodic structure. We also prove several corollaries, including applications to Chomp, and results concerning the computational complexity of calculating g-values in poset games.
منابع مشابه
PSPACE-completeness of the Weighted Poset Game
Poset game, which includes some famous games. e.g., Nim and Chomp as sub-games, is an important two-player impartial combinatorial game. The rule of the game is as follows: For a given poset (partial ordered set), each player intern chooses an element and the selected element and it’s descendants (elements succeeding it) are all removed from the poset. A player who choose the last element is th...
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