Homological Computations for Term Rewriting Systems
Homological Computations for Term Rewriting Systems
复制标题
术语重写系统的同调计算
DOI：
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发表时间：
2016
期刊：
影响因子：
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通讯作者：
S. Mimram
中科院分区：
文献类型：
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作者：
P. Malbos;S. Mimram
泛代数中的一个重要问题是寻找尽可能小的生成元和关系来表示代数理论。对于一个给定的理论，展示这些生成元和关系的数量的下界是一项困难的任务，因为它先验地需要考虑一个理论的所有可能的生成元集合，并且不存在通用的方法。在这篇文章中，我们解释了如何同调计算可以提供这样的下限，在一个系统的方式，并显示如何实际计算的情况下，由一个收敛的重写系统的理论介绍是已知的。我们还介绍了连贯的理论介绍的概念，以考虑更精细的同伦不变量。在某些方面，这项工作概括，长期重写系统，斯奎尔著名的同伦和同伦不变量字符串重写系统。
An important problem in universal algebra consists in finding presentations of algebraic theories by generators and relations, which are as small as possible. Exhibiting lower bounds on the number of those generators and relations for a given theory is a difficult task because it a priori requires considering all possible sets of generators for a theory and no general method exists. In this article, we explain how homological computations can provide such lower bounds, in a systematic way, and show how to actually compute those in the case where a presentation of the theory by a convergent rewriting system is known. We also introduce the notion of coherent presentation of a theory in order to consider finer homotopical invariants. In some aspects, this work generalizes, to term rewriting systems, Squier’s celebrated homological and homotopical invariants for string rewriting systems.