Scaling, Renormalization, and Universality in Combinatorial Games: The Geometry of Chomp
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- Friedman E.J., Landsberg A.S. (2007) Scaling, Renormalization, and Universality in Combinatorial Games: The Geometry of Chomp. In: Dress A., Xu Y., Zhu B. (eds) Combinatorial Optimization and Applications. COCOA 2007. Lecture Notes in Computer Science, vol 4616. Springer, Berlin, Heidelberg
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.
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