Reference. Regular planar monoidal languages

@article{EARNSHAW2024100963,
title = {Regular planar monoidal languages},
journal = {Journal of Logical and Algebraic Methods in Programming},
volume = {139},
pages = {100963},
year = {2024},
issn = {2352-2208},
doi = {https://doi.org/10.1016/j.jlamp.2024.100963},
url = {https://www.sciencedirect.com/science/article/pii/S235222082400021X},
author = {Matthew Earnshaw and Paweł Sobociński},
keywords = {Monoidal categories, String diagrams, Formal language theory, Automata, Cartesian restriction categories},
abstract = {We introduce regular languages of morphisms in free monoidal categories, with their associated grammars and automata. These subsume the classical theory of regular languages of words and trees, but also open up a much wider class of languages of planar string diagrams. We give a pumping lemma for monoidal languages, generalizing the one for words and trees. We use the algebra of monoidal and cartesian restriction categories to investigate the properties of regular monoidal languages, and provide sufficient conditions for their recognizability by deterministic monoidal automata.}
}