Algorithms for lattice games

Details Algorithms for lattice games Algorithms for lattice games

2011-05-26

arxiv.org/abs/1105.5413v1

Mathematics

Combinatorics

12 pages, no figures

Scientific paper

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.

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