Skip to Main content Skip to Navigation
New interface
Journal articles

Subshifts as models for MSO logic

Emmanuel Jeandel 1 Guillaume Theyssier 2 
1 CARTE - Theoretical adverse computations, and safety
Inria Nancy - Grand Est, LORIA - FM - Department of Formal Methods
Abstract : We study the Monadic Second Order (MSO) Hierarchy over colourings 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 characterise 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.
Document type :
Journal articles
Complete list of metadata
Contributor : Emmanuel Jeandel Connect in order to contact the contributor
Submitted on : Thursday, January 31, 2013 - 2:17:13 PM
Last modification on : Saturday, June 25, 2022 - 7:42:00 PM

Links full text



Emmanuel Jeandel, Guillaume Theyssier. Subshifts as models for MSO logic. Information and Computation, 2013, 225, pp.1-15. ⟨10.1016/j.ic.2013.01.003⟩. ⟨hal-00783099⟩



Record views