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.

翻译：令$G$为具有不可判定骨牌问题的群（例如$\mathbb{Z}^2$）。我们证明了所有非平凡动力性质对于sofic $G$-子移位均不可判定，指出此类结果对于SFT并不成立，并得到了关于$G$-SFT动力性质的、类似于Adian-Rabin定理的不可判定性结果。对于顺从群$G$，我们证明了拓扑熵无法通过SFT的表示进行计算，并给出了关于取值于偏序集的动力不变量的更一般结论。