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Subshifts, MSO logic, and collapsing hierarchies

Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) (2014) 8705 LNCS 111-122
DOI: 10.1007/978-3-662-44602-7_10
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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. © 2014 IFIP International Federation for Information Processing.

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Törmä, I. (2014). Subshifts, MSO logic, and collapsing hierarchies. In Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) (Vol. 8705 LNCS, pp. 111–122). Springer Verlag. https://doi.org/10.1007/978-3-662-44602-7_10

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