群的有理子集
Rational subsets of groups
摘要：
本文，第23章在“AutoMathA”手册，是专门研究合理的子集的群体，特别强调自动机理论的方法，以自动生成的子群的自由群体。事实上，Stallings的建设，关联有限逆自动机与每一个这样的子群，开创了一个完整的重写自由群算法，与连接到其他领域，如拓扑或动力学。另一个重要的向量在这一章是基本的伯努瓦定理，特点合理的子集的自由群。这个定理及其结果真正解释了为什么语言理论可以成功地应用于自由群的研究。（自由）群的有理子集可以在通过归纳证明陈述（与合理性概念无关的先验）中发挥重要作用。本章还包括更一般的群体，如虚拟自由群或图形群的相关结果。
英文摘要：
This text, Chapter 23 in the "AutoMathA" handbook, is devoted to the study of rational subsets of groups, with particular emphasis on the automata-theoretic approach to finitely generated subgroups of free groups. Indeed, Stallings' construction, associating a finite inverse automaton with every such subgroup, inaugurated a complete rewriting of free group algorithmics, with connections to other fields such as topology or dynamics. Another important vector in the chapter is the fundamental Benois' Theorem, characterizing rational subsets of free groups. The theorem and its consequences really explain why language theory can be successfully applied to the study of free groups. Rational subsets of (free) groups can play a major role in proving statements (a priori unrelated to the notion of rationality) by induction. The chapter also includes related results for more general classes of groups, such as virtually free groups or graph groups.
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