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Main Authors:	Matsui, Anna, Obi, Innocent, Sabbagh, Guillaume, Torres, Leo, Kessler, Diana, Meleiro, Juan F., Muroya, Koko
Format:	Preprint
Published:	2026
Subjects:	Category Theory Data Structures and Algorithms
Online Access:	https://arxiv.org/abs/2603.09433
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author	Matsui, Anna Obi, Innocent Sabbagh, Guillaume Torres, Leo Kessler, Diana Meleiro, Juan F. Muroya, Koko
author_facet	Matsui, Anna Obi, Innocent Sabbagh, Guillaume Torres, Leo Kessler, Diana Meleiro, Juan F. Muroya, Koko
contents	Critical pair analysis provides a convenient and computable criterion of confluence, which is a fundamental property in rewriting theory, for a wide variety of rewriting systems. Bonchi et al. showed validity of critical pair analysis for rewriting on string diagrams in symmetric monoidal categories. This work aims at automation of critical pair analysis for string diagram rewriting, and develops an algorithm that implements the core part of critical pair analysis. The algorithm enumerates all critical pairs of a given left-connected string diagram rewriting system, and it can be realised by concrete manipulation of hypergraphs. We prove correctness and exhaustiveness of the algorithm, for string diagrams in symmetric monoidal categories without a Frobenius structure.
format	Preprint
id	arxiv_https___arxiv_org_abs_2603_09433
institution	arXiv
publishDate	2026
record_format	arxiv
spellingShingle	A Critical Pair Enumeration Algorithm for String Diagram Rewriting Matsui, Anna Obi, Innocent Sabbagh, Guillaume Torres, Leo Kessler, Diana Meleiro, Juan F. Muroya, Koko Category Theory Data Structures and Algorithms Critical pair analysis provides a convenient and computable criterion of confluence, which is a fundamental property in rewriting theory, for a wide variety of rewriting systems. Bonchi et al. showed validity of critical pair analysis for rewriting on string diagrams in symmetric monoidal categories. This work aims at automation of critical pair analysis for string diagram rewriting, and develops an algorithm that implements the core part of critical pair analysis. The algorithm enumerates all critical pairs of a given left-connected string diagram rewriting system, and it can be realised by concrete manipulation of hypergraphs. We prove correctness and exhaustiveness of the algorithm, for string diagrams in symmetric monoidal categories without a Frobenius structure.
title	A Critical Pair Enumeration Algorithm for String Diagram Rewriting
topic	Category Theory Data Structures and Algorithms
url	https://arxiv.org/abs/2603.09433

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