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Von Neumann regularity, split epicness and elementary cellular automata (1804.03913v3)
Published 11 Apr 2018 in cs.FL, math.DS, and nlin.CG
Abstract: We show that a cellular automaton on a mixing subshift of finite type is a Von Neumann regular element in the semigroup of cellular automata if and only if it is split epic onto its image in the category of sofic shifts and block maps. It follows from [S.-T\"orm\"a, 2015] that Von Neumann regularity is decidable condition, and we decide it for all elementary CA.