Generalized Amazons is PSPACE-Complete
نویسندگان
چکیده
Amazons is a perfect information board game with simple rules and large branching factors. Two players alternately move chess queen-like pieces and block squares on a 10×10 playing field. The player who makes the last move wins. Amazons endgames usually decompose into independent subgames. Therefore, the game is a natural testbed for combinatorial game theory. It was known that determining the winner of simple generalized Amazons endgames is NP-equivalent. This paper presents two proofs for the PSPACEcompleteness of the generalized version of the full game.
منابع مشابه
Amazons is PSPACE-complete
Amazons is a board game which combines elements of Chess and Go. It has become popular in recent years, and has served as a useful platform for both game-theoretic study and AI games research. Buro [2] showed that simple Amazons endgames are NP-equivalent, leaving the complexity of the general case as an open problem. We settle this problem, by showing that deciding the outcome of an n×n Amazon...
متن کاملAmazons, Konane, and Cross Purposes are PSPACE-complete
Amazons is a board game which combines elements of Chess and Go. It has become popular in recent years, and has served as a useful platform for both game-theoretic study and AI games research. Buro [3] showed that simple Amazons endgames are NP-equivalent, leaving the complexity of the general case as an open problem. Konane is an ancient Hawaiian game, with moves similar to peg solitaire. Kona...
متن کاملThe Computational Complexity of Motion Planning
In this paper we show that a generalization of a popular motion planning puzzle called Lunar Lockout is computationally intractable. In particular, we show that the problem is PSPACE-complete. We begin with a review of NP-completeness and polynomial-time reductions, introduce the class PSPACE, and motivate the significance of PSPACE-complete problems. Afterwards, we prove that determining wheth...
متن کاملSimple Amazons Endgames and Their Connection to Hamilton Circuits in Cubic Subgrid Graphs
Amazons is a young board game with simple rules and a high branching factor, which makes it a suitable test-bed for planning research. This paper considers the computational complexity of amazons puzzles and restricted amazons endgames. We rst prove the NP{ completeness of the Hamilton circuit problem for cubic subgraphs of the integer grid. This result is then used to show that solving amazons...
متن کاملGeneralized Hex and Logical Characterizations of Polynomial Space We Consider a Particular Logical Characterization of the Complexity Class Pspace Using Rst-order Logic, with a Built-in Successor Relation, Extended
We answer a question posed by Makowsky and Pnueli and show that the logic (HEX) FO s ], where HEX is the operator (i.e., uniform sequence of Lindstrr om quantiiers) corresponding to the well-known PSPACE-complete decision problem Generalized Hex, collapses to the fragment HEX 1 FO s ] and, moreover, that this logic has a particular normal form which results in the problem HEX being complete for...
متن کامل