Quantifier Extensions of Multidimensional Sofic Shifts
Dynamical Systems
2014-07-24 v2 Formal Languages and Automata Theory
Abstract
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.
Keywords
Cite
@article{arxiv.1401.2294,
title = {Quantifier Extensions of Multidimensional Sofic Shifts},
author = {Ilkka Törmä},
journal= {arXiv preprint arXiv:1401.2294},
year = {2014}
}
Comments
15 pages, 3 figures. Submitted to Proceedings of the American Mathematical Society