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Context-Free Languages of String Diagrams

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arxiv 2404.10653 v1 pith:5SBHME46 submitted 2024-04-16 cs.FL math.CT

Matt Earnshaw , Mario Román This is my paper · ORCID
classification cs.FLmath.CT
keywords languagescontext-freediagramsstringmonoidalcategorieslanguageregular
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We introduce context-free languages of morphisms in monoidal categories, extending recent work on the categorification of context-free languages, and regular languages of string diagrams. Context-free languages of string diagrams include classical context-free languages of words, trees, and hypergraphs, when instantiated over appropriate monoidal categories. Using a contour-splicing adjunction, we prove a representation theorem for context-free languages of string diagrams: every such language arises as the image under a monoidal functor of a regular language of string diagrams.

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  1. Layered Monoidal Theories I: Diagrammatic Algebra and Applications

    cs.LO 2026-02 conditional novelty 6.0 of 10

    Layered monoidal theories let different abstraction levels of a system live in one string diagram with formal translations between layers.

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