Context-Free Languages of String Diagrams
Formal Languages and Automata Theory
2024-04-17 v1 Category Theory
Abstract
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.
Keywords
Cite
@article{arxiv.2404.10653,
title = {Context-Free Languages of String Diagrams},
author = {Matt Earnshaw and Mario Román},
journal= {arXiv preprint arXiv:2404.10653},
year = {2024}
}