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Subshifts, MSO Logic, and Collapsing Hierarchies
Published 27 Jun 2014 in math.DS, cs.FL, cs.LO, and math.LO | (1406.7155v1)
Abstract: We use monadic second-order logic to define two-dimensional subshifts, or sets of colorings of the infinite plane. We present a natural family of quantifier alternation hierarchies, and show that they all collapse to the third level. In particular, this solves an open problem of [Jeandel & Theyssier 2013]. The results are in stark contrast with picture languages, where such hierarchies are usually infinite.
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