Context-Free Languages of String Diagrams

TL;DR

This paper extends the concept of context-free languages to string diagrams within monoidal categories, providing a categorical framework that generalizes classical language classes and establishing a representation theorem for these languages.

Contribution

It introduces a new class of context-free languages of string diagrams and proves a representation theorem linking them to regular languages via monoidal functors.

Findings

Includes classical languages like words, trees, hypergraphs as special cases.

Establishes a representation theorem using contour-splicing adjunction.

Generalizes language classes within a categorical framework.

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.