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 of finite type (SFTs) in dimension d > 1. In particular, we prove that the factorization problem is Sigma^0_3-complete and that the conjugacy and embedding problems are Sigma^0_1-complete in the arithmetical hierarchy.
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