Monoidal Width

IF 0.6 4区数学 Q4 COMPUTER SCIENCE, THEORY & METHODS

Logical Methods in Computer Science Pub Date : 2023-09-04 DOI:10.46298/lmcs-19(3:15)2023

Elena Di Lavore, Paweł Sobociński

引用次数: 2

Abstract

We introduce monoidal width as a measure of complexity for morphisms in monoidal categories. Inspired by well-known structural width measures for graphs, like tree width and rank width, monoidal width is based on a notion of syntactic decomposition: a monoidal decomposition of a morphism is an expression in the language of monoidal categories, where operations are monoidal products and compositions, that specifies this morphism. Monoidal width penalises the composition operation along ``big'' objects, while it encourages the use of monoidal products. We show that, by choosing the correct categorical algebra for decomposing graphs, we can capture tree width and rank width. For matrices, monoidal width is related to the rank. These examples suggest monoidal width as a good measure for structural complexity of processes modelled as morphisms in monoidal categories.

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单项宽度

我们引入一元宽度作为一元范畴中态射复杂性的度量。受众所周知的图的结构宽度度量的启发，如树宽度和秩宽度，一元宽度是基于一个语法分解的概念:一个态射的一元分解是在一元范畴的语言中的表达式，其中的操作是一元积和组合，它指定了这个态射。单面宽度惩罚沿着“大”对象的构图操作，而鼓励使用单面产品。我们表明，通过选择正确的分类代数来分解图，我们可以捕获树的宽度和秩的宽度。对于矩阵，单轴宽度与秩有关。这些例子表明，单线宽度是衡量单线范畴中模态过程结构复杂性的好方法。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Logical Methods in Computer Science 工程技术-计算机：理论方法

CiteScore

1.80

自引率

0.00%

发文量

105

审稿时长

6-12 weeks

期刊介绍： Logical Methods in Computer Science is a fully refereed, open access, free, electronic journal. It welcomes papers on theoretical and practical areas in computer science involving logical methods, taken in a broad sense; some particular areas within its scope are listed below. Papers are refereed in the traditional way, with two or more referees per paper. Copyright is retained by the author. Topics of Logical Methods in Computer Science: Algebraic methods Automata and logic Automated deduction Categorical models and logic Coalgebraic methods Computability and Logic Computer-aided verification Concurrency theory Constraint programming Cyber-physical systems Database theory Defeasible reasoning Domain theory Emerging topics: Computational systems in biology Emerging topics: Quantum computation and logic Finite model theory Formalized mathematics Functional programming and lambda calculus Inductive logic and learning Interactive proof checking Logic and algorithms Logic and complexity Logic and games Logic and probability Logic for knowledge representation Logic programming Logics of programs Modal and temporal logics Program analysis and type checking Program development and specification Proof complexity Real time and hybrid systems Reasoning about actions and planning Satisfiability Security Semantics of programming languages Term rewriting and equational logic Type theory and constructive mathematics.