Regular planar monoidal languages

Regular planar monoidal languages

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 mo...

Ausführliche Beschreibung

Gespeichert in:
Bibliographische Detailangaben
Veröffentlicht in:Journal of logical and algebraic methods in programming 2024-06, Vol.139, p.100963, Article 100963
Hauptverfasser: Earnshaw, Matthew, Sobociński, Paweł
Format: Artikel
Sprache:eng
Schlagworte:
Automata
Cartesian restriction categories
Formal language theory
Monoidal categories
String diagrams
Online-Zugang:Volltext
Tags: Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
Beschreibung
Zusammenfassung: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.
ISSN:2352-2208
DOI:10.1016/j.jlamp.2024.100963