Amazons is PSPACE-complete
| dc.creator | Hearn, Robert A. | |
| dc.date | 2005-02-02 | |
| dc.date.accessioned | 2026-07-07T03:22:27Z | |
| dc.date.available | 2026-07-07T03:22:27Z | |
| dc.description | 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. | |
| dc.description | 7 pages, 5 figures. For 2005 Combinatorial Game Theory Workshop at BIRS | |
| dc.identifier | https://arxiv.org/abs/cs/0502013 | |
| dc.identifier | http://arxiv.org/abs/cs/0502013 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/32604 | |
| dc.subject | Computational Complexity | |
| dc.subject | Computer Science and Game Theory | |
| dc.subject | F.2.2 | |
| dc.title | Amazons is PSPACE-complete | |
| dc.type | text |