TWO-DIMENSIONAL LANGUAGES AND CELLULAR AUTOMATA

Abstract

Space-time diagrams of a one-dimensional cellular automaton can be visualized as half-plane arrays of symbols. The set of rectangular blocks extracted from such arrays forms a two-dimensional (picture) language. We initiate a study of cellular automata through the associated two dimensional languages by investigating cellular automata whose two-dimensional languages are factorial-local. We show that these cellular automata have the same characterization as one-sided cellular automata with SFT traces.