群中子移位的周期构型
Periodic configurations of subshifts on groups
摘要：
本文研究了定义在生成群（的Cayley图）上的移位空间的周期位形的密度。我们证明了在剩余有限群上的全移位和在阿贝尔群上的群移位空间中，周期构形是稠密的。在一维情况下，我们证明了不可约sofic位移的密度。在这方面，我们研究了元胞自动机和局部自映射的超接性。本文还研究了有限型移位空间的一些相关的判定问题。
英文摘要：
We study the density of periodic configurations for shift spaces defined on (the Cayley graph of) a finitely generated group. We prove that in the case of a full shift on a residually finite group and in that of a group shift space on an abelian group, the periodic configurations are dense. In the one-dimensional case we prove the density for irreducible sofic shifts. In connection with this we study the surjunctivity of cellular automata and local selfmappings. Some related decision problems for shift spaces of finite type are also investigated.
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