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In this paper, we de ne cellular automata on a grid of the hyperbolic plane, based on the tessellation obtained from the regular pentagon with right angles. Taking advantage of the properties of that grid, we show that 3-SAT can be solved in polynomial time in that setting, and then we extend that result for any NP problem. Several directions starting from that result are indicated. Categories: F.1.1, F.1.3

A Polynomial Solution for 3-SAT in the Space of Cellular Automata in the Hyperbolic Plane