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Hardness of conjugacy, embedding and factorization of multidimensional subshifts. (English) Zbl 1328.68074
Summary: Subshifts of finite type are sets of colorings of the plane defined by local constraints. They can be seen as a discretization of continuous dynamical systems. We investigate here the hardness of deciding factorization, conjugacy and embedding of subshifts in dimensions $$d > 1$$ for subshifts of finite type and sofic shifts and in dimensions $$d \geq 1$$ for effective shifts. In particular, we prove that the conjugacy, factorization and embedding problems are $$\Sigma_3^0$$-complete for sofic and effective subshifts and that they are $$\Sigma_1^0$$-complete for SFTs, except for factorization which is also $$\Sigma_3^0$$-complete.

##### MSC:
 68Q17 Computational difficulty of problems (lower bounds, completeness, difficulty of approximation, etc.) 37B50 Multi-dimensional shifts of finite type, tiling dynamics (MSC2010)
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