Year: 2020
Type: preprint
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.
Source: arXiv (Cornell University)
Authors: Song, Yerim, Grochow, Joshua A.
Institution: University of Colorado Boulder
Language: English
Subfield: Computational Theory and Mathematics
Field: Computer Science
Domain: Physical Sciences
Open Access status: green
Funder: National Science Foundation
OpenAlex ID: W3114792244