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Multidimensional tilings and MSO logic

Published 23 May 2025 in cs.FL, math.DS, and math.LO | (2505.17699v1)

Abstract: We define sets of coulourings of the infinite discrete plane using monadic second order (MSO) formulas. We determine the complexity of deciding whether such a formula defines a subshift, parametrized on the quantifier alternation complexity of the formula. We also study the complexities of languages of MSO-definable sets, giving either an exact classification or upper and lower bounds for each quantifier alternation class.

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Authors (2)

  1. Rémi Pallen 
  2. Ilkka Törmä 

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