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Subshifts as models for MSO logic. (English) Zbl 1435.03064
Summary: We study the Monadic Second Order (MSO) Hierarchy over colorings of the discrete plane, and draw links between classes of formula and classes of subshifts. We give a characterization of existential MSO in terms of projections of tilings, and of universal sentences in terms of combinations of “pattern counting” subshifts. Conversely, we characterize logic fragments corresponding to various classes of subshifts (subshifts of finite type, sofic subshifts, all subshifts). Finally, we show by a separation result how the situation here is different from the case of tiling pictures studied earlier by Giammarresi et al.

MSC:
03C90 Nonclassical models (Boolean-valued, sheaf, etc.)
03B16 Higher-order logic
37B10 Symbolic dynamics
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