2018/09/25 by Gács, Péter, Törmä, Ilkka · 3 citations
#37B15 #60J05 #60K35 #Discrete Mathematics (cs.DM) #FOS: Computer and information sciences #FOS: Mathematics #Probability (math.PR)
paper · doi:10.48550/arxiv.1809.09503
Eroders are monotonic cellular automata with a linearly ordered state set that eventually wipe out any finite island of nonzero states. One-dimensional eroders were studied by Gal'perin in the 1970s, who presented a simple combinatorial characterization of the class. The multi-dimensional case has been studied by Toom and others, but no such characterization has been found. We prove a similar characterization for those one-dimensional monotonic cellular automata that are eroders even in the presence of random noise.