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On a Rice theorem for dynamical properties of SFTs on groups (2401.10347v2)

Published 18 Jan 2024 in math.DS, cs.IT, math.CO, math.GR, math.IT, and math.LO

Abstract: Let $G$ be a group with undecidable domino problem (such as $\mathbb{Z}2$). We prove the undecidability of all nontrivial dynamical properties for sofic $G$-subshifts, that such a result fails for SFTs, and an undecidability result for dynamical properties of $G$-SFTs similar to the Adian-Rabin theorem. For $G$ amenable we prove that topological entropy is not computable from presentations of SFTs, and a more general result for dynamical invariants taking values in partially ordered sets.

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