Geodesic rewriting systems and pregroups
Geodesic rewriting systems and pregroups
复制标题
测地线重写系统和预组
DOI：
10.1007/978-3-7643-9911-5_3
复制
发表时间：
2009
期刊：
影响因子：
--
通讯作者：
A. Miasnikov
中科院分区：
文献类型：
--
作者：
V. Diekert;A. Duncan;A. Miasnikov
在本文中，我们研究重写系统的群体和monoid，集中在有限收敛系统可能很难找到或不存在的情况。我们认为系统没有长度增加的规则，并融合，然后系统中的长度减少的规则导致测地线。结合这些性质，我们到达我们的主要研究对象，我们称之为测地线完美重写系统。我们表明，这些都是行为良好，方便使用，并给出了几个例子的类的群体，他们可以从自然的介绍。我们描述了构建此类系统的Knuth-Bendix完成过程，展示了如何在Stallings的预群的帮助下找到它们，以及如何相反地用于构建此类预群。
In this paper we study rewriting systems for groups and monoids, focusing on situations where finite convergent systems may be difficult to find or do not exist. We consider systems which have no length increasing rules and are confluent and then systems in which the length reducing rules lead to geodesics. Combining these properties we arrive at our main object of study which we call geodesically perfect rewriting systems. We show that these are well-behaved and convenient to use, and give several examples of classes of groups for which they can be constructed from natural presentations. We describe a Knuth-Bendix completion process to construct such systems, show how they may be found with the help of Stallings' pregroups and conversely may be used to construct such pregroups.