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Quantifier extensions of multidimensional sofic shifts. (English) Zbl 1353.37037
Summary: 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.

##### MSC:
 37B50 Multi-dimensional shifts of finite type, tiling dynamics (MSC2010) 68Q05 Models of computation (Turing machines, etc.) (MSC2010)
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