Paper Info
Title
Amazons is PSPACE-complete
Abstract
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 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 x n Amazons position is PSPACE-hard. We give a reduction from one of the PSPACE-complete two-player formula games described by Schaefer. Since the number of moves in an Amazons game is polynomially bounded (unlike Chess and Go), Amazons is in PSPACE. It is thus on a par with other two-player, bounded-move, perfect-information games such as Hex, Othello, and Kayles. Our construction also provides an alternate proof that simple Amazons endgames are NP-equivalent. Our reduction uses a number of amazons polynomial in the input formula length; a remaining open problem is the complexity of Amazons when only a constant number of amazons is used.
Year
Venue
Keywords
2005
Clinical Orthopaedics and Related Research
computational complexity,game theory
Field
DocType
Volume
Discrete mathematics,Combinatorics,Kayles,Open problem,Polynomial,PSPACE-complete,PSPACE,Mathematics,Bounded function
Journal
abs/cs/050
Citations 
PageRank 
References 
4
0.56
5
Authors
1
Name
Order
Citations
PageRank
Robert A. Hearn116920.52