Scaling, renormalization, and universality in combinatorial games: The geometry of chomp

Abstract

Combinatorial games pose an extreme challenge to combinatorial optimization. Several combinatorial games have been shown to be PSPACEhard and many more are believed to be so. In this paper, we present a new approach to analyzing combinatorial games, which differs dramatically from current approaches. Using the combinatorial game Chomp as a model system, we employ ideas from physics and dynamical systems theory to unveil deep connections between such games and nonlinear phenomena commonly seen in nature. © Springer-Verlag Berlin Heidelberg 2007.