Subshifts, Languages and Logic
Emmanuel Jeandel (LIF), Guillaume Theyssier (LM-Savoie)
TL;DR
This paper explores the Monadic Second Order (MSO) logic hierarchy over infinite tilings, providing characterizations of existential MSO and various classes of infinite pictures such as subshifts.
Contribution
It offers new logical characterizations of tiling classes and connects MSO logic fragments with classes of infinite pictures, advancing understanding of tiling and logic.
Findings
Characterization of existential MSO in terms of tilings and projections
Logical fragment characterizations of subshifts of finite type and sofic subshifts
Bridging tiling theory with MSO logic hierarchies
Abstract
We study the Monadic Second Order (MSO) Hierarchy over infinite pictures, that is tilings. We give a characterization of existential MSO in terms of tilings and projections of tilings. Conversely, we characterise logic fragments corresponding to various classes of infinite pictures (subshifts of finite type, so?c subshifts).
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