字符串图重写中的关键对枚举算法

基于递减性的串重写系统的一致性

Coherence of string rewriting systems by decreasingness

Squier引入了同伦方法来描述合流终止弦重写系统的重写约简之间的所有关系。从一个字符串重写系统，他构建了一个$2$维组合复杂的$2$细胞产生的关系引起的重写规则。当重写系统是合流终止的时，该复形的同伦可以用重写系统的临界分支所诱导的合流图来刻画。这样的构造现在被用来解决使用字符串重写系统的幺半群的相干问题。在这篇文章中，我们展示了如何削弱终止假设的描述重写约简之间的所有关系。我们的构造使用了van Oostrom引入的递减方法。本文引入了递减二维多道图的概念，并给出了递减多道图可一致扩展的充分条件。特别是，我们展示了如何融合和准终止测谎仪可以扩展到一个连贯的演示。

String Diagram Rewrite Theory II: Rewriting with Symmetric Monoidal Structure

Symmetric monoidal theories (SMTs) generalise algebraic theories in a way that make them suitable to express resource-sensitive systems, in which variables cannot be copied or discarded at will. In SMTs, traditional tree-like terms are replaced by string diagrams, topological entities that can be intuitively thoughts as diagrams of wires and boxes. Recently, string diagrams have become increasingly popular as a graphical syntax to reason about computational models across diverse fields, including programming language semantics, circuit theory, quantum mechanics, linguistics, and control theory…

String Diagram Rewrite Theory I: Rewriting with Frobenius Structure

String diagrams are a powerful and intuitive graphical syntax, originated in the study of symmetric monoidal categories. In the last few years, they have found application in the modelling of various computational structures, in fields as diverse as Computer Science, Physics, Control Theory, Linguistics, and Biology. In many such proposals, the transformations of the described systems are modelled as rewrite rules of diagrams. These developments demand a mathematical foundation for string diagram rewriting: whereas rewrite theory for terms is well-understood, the two-dimensional nature of stri…

具有交换（余）幺半群结构的对称幺半群范畴的重写

Rewriting for Symmetric Monoidal Categories with Commutative (Co)Monoid Structure

本文研究弦图重写中比完整 Frobenius 结构更弱的交换幺半群结构，并通过超图双推出重写的可靠且完备解释刻画了模去交换幺半群等式的弦图重写。

Monoid的Logged重写

Logged Rewriting for Monoids

重写系统是在一组给定的术语上的一组方程，称为规则，其表征计算系统，并且是用于提供方程理论的决策过程的强大的通用方法，其基于用其他术语替换表达式的子项的原则。特别是，一个字符串重写系统通常与幺半群表示相关联。在第一级的问题是决定哪些组合的发电机是等价的，在给定的规则; Knuth-Benzynn完成的字符串重写系统是解决这个问题的最成功的机制之一。在第二个层次上，问题涉及确定哪些规则组合是等价的。记录重写是一种技术，它不仅转换字符串，而且根据原始规则系统记录转换。幺半群的组合、同伦和同调有限性条件之间的关系促使我们考虑使用计算机友好的重写系统从幺半群表示计算同伦和同调结构。

Confluence of algebraic rewriting systems

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 betw…