Algorithms for lattice games
Combinatorics
2011-05-30 v1 Commutative Algebra
Abstract
This paper provides effective methods for the polyhedral formulation of impartial finite combinatorial games as lattice games. Given a rational strategy for a lattice game, a polynomial time algorithm is presented to decide (i) whether a given position is a winning position, and to find a move to a winning position, if not; and (ii) to decide whether two given positions are congruent, in the sense of mis\`ere quotient theory. The methods are based on the theory of short rational generating functions.
Cite
@article{arxiv.1105.5413,
title = {Algorithms for lattice games},
author = {Alan Guo and Ezra Miller},
journal= {arXiv preprint arXiv:1105.5413},
year = {2011}
}
Comments
12 pages, no figures