2014/01/10 by Ilkka Törmä, Törmä, Ilkka
Computer Science · Mathematics · #37B50 #Dynamical Systems (math.DS) #FOS: Computer and information sciences #FOS: Mathematics #Formal Languages and Automata Theory (cs.FL) #cs.FL #math.DS #msc:37B50
paper · pdf · doi:10.48550/arxiv.1401.2294
15 pages, 3 figures. Submitted to Proceedings of the American Mathematical Society
arxiv created 2014/07/23 · arxiv updated 2014/07/24
We define a pair of simple combinatorial operations on subshifts, called existential and universal extensions, and study their basic properties. We prove that the existential extension of a sofic shift by another sofic shift is always sofic, and the same holds for the universal extension in one dimension. However, we also show by a construction that universal extensions of two-dimensional sofic shifts may not be sofic, even if the subshift we extend by is very simple.