We propose a definition of graph subshifts of finite type that can be seen as extending both the notions of subshifts of finite type from classical symbolic dynamics and finitely presented groups from combinatorial group theory. These are sets of graphs that are defined by forbidding finitely many local patterns. In this paper, we focus on the question whether such local conditions can enforce a specific support graph, and thus relate the model to classical symbolic dynamics. We prove that the subshifts that contain only infinite graphs are either aperiodic, or feature no residual finiteness of their period group, yielding non-trivial examples as well as two natural undecidability theorems.

翻译：我们提出了一种有限型图子移位的定义，该定义可视为同时推广了经典符号动力学中的有限型子移位概念和组合群论中的有限表示群。这些图子移位是由禁止有限多个局部模式所定义的图集合。本文重点探讨此类局部条件是否能强制规定特定的支撑图，从而将模型与经典符号动力学联系起来。我们证明了仅包含无限图的子移位要么是非周期的，要么其周期群不具备剩余有限性，由此既得到非平凡的例子，也得出两个自然的不可判定性定理。