A Critical Pair Enumeration Algorithm for String Diagram Rewriting
This work provides an incremental automation tool for rewriting theory, specifically for researchers in formal methods or category theory dealing with string diagrams.
The paper tackled the problem of automating critical pair analysis for string diagram rewriting by developing an algorithm that enumerates all critical pairs for left-connected systems, proving its correctness and exhaustiveness for symmetric monoidal categories without a Frobenius structure.
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.