论文标题
线性重写系统的策略：与并行重写和参与部门链接
Strategies for linear rewriting systems: link with parallel rewriting and involutive divisions
论文作者
论文摘要
我们研究了重写系统的重写系统，其基本术语在给定字段上配备了矢量空间结构。我们介绍了并行重写关系，这些关系正在重写与向量空间结构兼容的关系以及重写策略，这些策略包括为向量空间的每个可降低基础元素选择一个重写步骤。使用这些概念，我们介绍了s互惠属性，并表明它意味着汇合。我们根据策略推断出钻石的引理证明。我们用重写系统的重写系统来说明我们的一般框架，这是有理函数领域的向量空间。特别是，我们表明，参与部门会导致对理性Weyl代数的重写策略，并使用$ s $ confluence属性，我们表明，参与集合会导致汇合重写系统，而不是理性的Weyl代数。
We study rewriting systems whose underlying set of terms is equipped with a vector space structure over a given field. We introduce parallel rewriting relations, which are rewriting relations compatible with the vector space structure, as well as rewriting strategies, which consist in choosing one rewriting step for each reducible basis element of the vector space. Using these notions, we introduce the S-confluence property and show that it implies confluence. We deduce a proof of the diamond's lemma, based on strategies. We illustrate our general framework with rewriting systems over rational Weyl algebras, that are vector spaces over a field of rational functions. In particular, we show that involutive divisions induce rewriting strategies over rational Weyl algebras, and using the $S$-confluence property, we show that involutive sets induce confluent rewriting systems over rational Weyl algebras.
