Mathematics - Category Theory https:// arxiv.org/list/math.CT/new Not affiliated with arXiv. Run by @ vela with https:// github.com/so-okada/toXiv Other bots: https:// mastoxiv.page/@vela/1096423875 63304551 You can filter by the keyword toXiv_bot_toot to hide all toXiv bot toots. # arXiv # Mathematics # CategoryTheory text-search: https:// tootfinder.ch
Mathematics - Category Theory https:// arxiv.org/list/math.CT/new Not affiliated with arXiv. Run by @ vela with https:// github.com/so-okada/toXiv Other bots: https:// mastoxiv.page/@vela/1096423875 63304551 You can filter by the keyword toXiv_bot_toot to hide all toXiv bot toots. # arXiv # Mathematics # CategoryTheory text-search: https:// tootfinder.ch
A Critical Pair Enumeration Algorithm for String Diagram Rewriting
Anna Matsui (Johns Hopkins University, USA), Innocent Obi (University of Washington, USA), Guillaume Sabbagh (University of Technology of Compi\`egne, France), Leo Torres (Universidad Nacional de C\`ordoba, Argentina), Diana Kessler (Tallinn University of Technology, Estonia), Juan F. Meleiro (University of S\~ao Paulo, Brazil), Koko Muroya (National Institute of Informatics, Japan,Ochanomizu University, Japan)
https://arxiv.org/abs/2603.09433 https://arxiv.org/pdf/2603.09433 https://arxiv.org/html/2603.09433
arXiv:2603.09433v1 Announce Type: new
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.
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