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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Törmä, I. (2014). Subshifts, MSO Logic, and Collapsing Hierarchies. In: Diaz, J., Lanese, I., Sangiorgi, D. (eds) Theoretical Computer Science. TCS 2014. Lecture Notes in Computer Science, vol 8705. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-44602-7_10
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DOI: https://doi.org/10.1007/978-3-662-44602-7_10
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