一位侧移位映射的共轭关系是非树形的

The complexity of the topological conjugacy problem for Toeplitz subshifts

In this paper, we analyze the Borel complexity of the topological conjugacy relation on Toeplitz subshifts. More specifically, we prove that topological conjugacy of Toeplitz subshifts with separated holes is hyperfinite. Indeed, we show that the topological conjugacy relation is hyperfinite on a larger class of Toeplitz subshifts which we call Toeplitz subshifts with growing blocks. This result provides a partial answer to a question asked by Sabok and Tsankov.

Toeplitz子移位拓扑共轭的复杂性

On the complexity of topological conjugacy of Toeplitz subshifts

本文研究了剩余有限群$G$的Toeplitz子移位的共轭性等价关系的描述集合论复杂性。一方面，我们证明了，如果$G = \mathbb{Z}$，那么具有分离洞的Toeplitz子移位上的拓扑共轭是顺从的。相反，如果$G$是不顺从的，则Toeplitz $G$ -子移位的共轭性是不顺从的等价关系。结果的动机是一个一般性的问题，问高，杰克逊和苏厄德，关于复杂的共轭最小，自由子移位的可数群。

多维子移位之间关系的参数复杂性

Parametrized complexity of relations between multidimensional subshifts

本文研究了多维子移位之间关系的参数复杂性，发现某些参数选择使问题达到最大难度，并揭示了多维SFT中非平凡可判定问题的存在。

有限秩 Toeplitz 子移位

Toeplitz subshifts of finite rank

本文研究有限拓扑秩 Toeplitz 子移位，通过构造反例否定刻画问题并证明强 Toeplitz 子移位集合的通有性，同时确定拓扑秩 2 情形下共轭等分类问题的复杂度，并刻画其自同构群结构。

Conjugacy of reversible cellular automata and one-head machines

We show that conjugacy of reversible cellular automata is undecidable, whether the conjugacy is to be performed by another reversible cellular automaton or by a general homeomorphism. This gives rise to a new family of finitely-generated groups with undecidable conjugacy problems, whose descriptions arguably do not involve any type of computation. For many automorphism groups of subshifts, as well as the group of asynchronous transducers and the homeomorphism group of the Cantor set, our result implies the existence of two elements such that every finitely-generated subgroup containing both ha…