The symmetric Post Correspondence Problem, and errata for the freeness problem for matrix semigroups

自动机半群的自由性问题

The Freeness Problem for Automaton Semigroups

本文解决了Grigorchuk等人提出的开放问题，证明自动机半群和幺半群的自由性问题不可判定，通过将Post对应问题编码到其中实现，且输入字母表可限制为恒定大小，还得到了其他半群概念的不可判定性结果。

Automaton Semigroups and Groups: On the Undecidability of Problems Related to Freeness and Finiteness

In this paper, we study algorithmic problems for automaton semigroups and automaton groups related to freeness and finiteness. In the course of this study, we also exhibit some connections between the algebraic structure of automaton (semi)groups and their dynamics on the boundary. First, we show that it is undecidable to check whether the group generated by a given invertible automaton has a positive relation, i.e. a relation p = 1 such that p only contains positive generators. Besides its obvious relation to the freeness of the group, the absence of positive relations has previously been stu…

仿射群的随机自由半群

Random free semigroups of affine groups

研究可解非幂零情形下半群的随机自由性，聚焦相关仿射模型，表明自由性长期行为由阿贝尔影子决定，证明结合仿射随机游走局部收缩定理与乒乓论证。