Regular Monoidal Languages

Authors Matthew Earnshaw , Paweł Sobociński

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Author Details

Matthew Earnshaw
  • Department of Software Science, Tallinn University of Technology, Estonia
Paweł Sobociński
  • Department of Software Science, Tallinn University of Technology, Estonia


We would like to thank Ed Morehouse for extensive discussions concerning this work, and Tobias Heindel for discussion of his erstwhile project that partially inspired ours.

Cite AsGet BibTex

Matthew Earnshaw and Paweł Sobociński. Regular Monoidal Languages. In 47th International Symposium on Mathematical Foundations of Computer Science (MFCS 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 241, pp. 44:1-44:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2022)


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 over string diagrams. We use the algebra of monoidal categories to investigate the properties of regular monoidal languages, and provide sufficient conditions for their recognizability by deterministic monoidal automata.

Subject Classification

ACM Subject Classification
  • Theory of computation → Formal languages and automata theory
  • Theory of computation → Categorical semantics
  • monoidal categories
  • string diagrams
  • formal language theory
  • cartesian restriction categories


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