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arXiv · 2012.12153

An Improved Algorithm for Coarse-Graining Cellular Automata

Yerim Song·Joshua A. Grochow
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Abstract

In studying the predictability of emergent phenomena in complex systems, Israeli & Goldenfeld (Phys. Rev. Lett., 2004; Phys. Rev. E, 2006) showed how to coarse-grain (elementary) cellular automata (CA). Their algorithm for finding coarse-grainings of supercell size $N$ took doubly-exponential $2^{2^N}$-time, and thus only allowed them to explore supercell sizes $N \leq 4$. Here we introduce a new, more efficient algorithm for finding coarse-grainings between any two given CA that allows us to systematically explore all elementary CA with supercell sizes up to $N=7$, and to explore individual examples of even larger supercell size. Our algorithm is based on a backtracking search, similar to the DPLL algorithm with unit propagation for the NP-complete problem of Boolean Satisfiability.

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Yerim Song, Joshua A. Grochow. 2020-12-22. An Improved Algorithm for Coarse-Graining Cellular Automata. https://arxiv.org/abs/2012.12153

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