In this article we construct asynchronous and sometimes synchronous automatic structures for amalgamated products and HNN extensions of groups that are strongly asynchronously (or synchronously) coset automatic with respect to the associated automatic subgroups, subject to further geometric conditions. These results are proved in the general context of fundamental groups of graphs of groups. The hypotheses of our closure results are satisfied in a variety of examples such as Artin groups of sufficiently large type, Coxeter groups, virtually abelian groups, and groups that are hyperbolic relative to virtually abelian subgroups.

中文翻译：

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组图的自动化

在本文中，我们为合并产品和组的 HNN 扩展构建异步和有时同步的自动结构，这些组相对于关联的自动子组是强异步（或同步）陪集自动的，受进一步几何条件的约束。这些结果在群的图的基本群的一般上下文中得到证明。我们的闭包结果的假设在各种示例中得到满足，例如足够大的 Artin 群、Coxeter 群、虚拟阿贝尔群以及相对于虚拟阿贝尔子群呈双曲线的群。