Combinatorial Optimization and Applications

Volume 4616 of the series Lecture Notes in Computer Science pp 200-207

Scaling, Renormalization, and Universality in Combinatorial Games: The Geometry of Chomp

  • Eric J. FriedmanAffiliated withSchool of ORIE, Cornell University, Ithaca, NY 14853
  • , Adam Scott LandsbergAffiliated withJoint Science Department, Claremont McKenna, Pitzer, and Scripps Colleges, Claremont, California 91711

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Combinatorial games pose an extreme challenge to combinatorial optimization. Several combinatorial games have been shown to be PSPACE-hard 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.