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Abstract: We study the Monadic Second Order MSO Hierarchy over colourings of thediscrete plane, and draw links between classes of formula and classes ofsubshifts. We give a characterization of existential MSO in terms ofprojections of tilings, and of universal sentences in terms of combinations of-pattern counting- subshifts. Conversely, we characterise logic fragmentscorresponding to various classes of subshifts subshifts of finite type, soficsubshifts, all subshifts. Finally, we show by a separation result how thesituation here is different from the case of tiling pictures studied earlier byGiammarresi et al.



Author: Emmanuel Jeandel LIF, Guillaume Theyssier LAMA

Source: https://arxiv.org/







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