代数重写系统的汇流
Confluence of algebraic rewriting systems
摘要：
代数结构上的收敛重写系统给出了解决判定问题、证明一致性结果和计算同调不变量的方法。这些方法是基于高维扩展的临界分支引理，证明了当地的汇合的临界分支。代数结构（如群或线性代数）上的重写系统的局部收敛性分析由于底层的代数公理而变得复杂。本文介绍了代数测谎模的结构，形式化的代数重写系统的规则和固有的代数公理之间的相互作用，我们展示了一个关键的分支引理代数测谎。我们推导出一个临界分支引理重写系统的代数模型，其公理指定的收敛模重写系统。我们说明了我们的建设字符串，线性和组重写系统。
英文摘要：
Convergent rewriting systems on algebraic structures give methods to solve decision problems, to prove coherence results, and to compute homological invariants. These methods are based on higher-dimensional extensions of the critical branching lemma that proves local confluence from confluence of the critical branchings. The analysis of local confluence of rewriting systems on algebraic structures, such as groups or linear algebras, is complicated because of the underlying algebraic axioms. This article introduces the structure of algebraic polygraph modulo that formalizes the interaction between the rules of an algebraic rewriting system and the inherent algebraic axioms, and we show a critical branching lemma for algebraic polygraphs. We deduce a critical branching lemma for rewriting systems on algebraic models whose axioms are specified by convergent modulo rewriting systems. We illustrate our constructions for string, linear, and group rewriting systems.
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