A Critical Pair Enumeration Algorithm for String Diagram Rewriting
Abstract
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.
Keywords
Cite
@article{arxiv.2603.09433,
title = {A Critical Pair Enumeration Algorithm for String Diagram Rewriting},
author = {Anna Matsui and Innocent Obi and Guillaume Sabbagh and Leo Torres and Diana Kessler and Juan F. Meleiro and Koko Muroya},
journal= {arXiv preprint arXiv:2603.09433},
year = {2026}
}
Comments
In Proceedings ACT 2025, arXiv:2603.07595