@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.}
}

@InProceedings{earnshaw_et_al:LIPIcs.CSL.2024.25,
  author =	{Earnshaw, Matt and Hefford, James and Rom\'{a}n, Mario},
  title =	{{The Produoidal Algebra of Process Decomposition}},
  booktitle =	{32nd EACSL Annual Conference on Computer Science Logic (CSL 2024)},
  pages =	{25:1--25:19},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-310-2},
  ISSN =	{1868-8969},
  year =	{2024},
  volume =	{288},
  editor =	{Murano, Aniello and Silva, Alexandra},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.CSL.2024.25},
  URN =		{urn:nbn:de:0030-drops-196688},
  doi =		{10.4230/LIPIcs.CSL.2024.25},
  annote =	{Keywords: monoidal categories, profunctors, lenses, duoidal categories}
}

@InProceedings{earnshaw_et_al:LIPIcs.MFCS.2023.43,
  author =	{Earnshaw, Matthew and Soboci\'{n}ski, Pawe{\l}},
  title =	{{String Diagrammatic Trace Theory}},
  booktitle =	{48th International Symposium on Mathematical Foundations of Computer Science (MFCS 2023)},
  pages =	{43:1--43:15},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-292-1},
  ISSN =	{1868-8969},
  year =	{2023},
  volume =	{272},
  editor =	{Leroux, J\'{e}r\^{o}me and Lombardy, Sylvain and Peleg, David},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.MFCS.2023.43},
  URN =		{urn:nbn:de:0030-drops-185770},
  doi =		{10.4230/LIPIcs.MFCS.2023.43},
  annote =	{Keywords: symmetric monoidal categories, Mazurkiewicz traces, asynchronous automata}
}

@InProceedings{earnshaw_et_al:LIPIcs.MFCS.2022.44,
  author =	{Earnshaw, Matthew and Soboci\'{n}ski, Pawe{\l}},
  title =	{{Regular Monoidal Languages}},
  booktitle =	{47th International Symposium on Mathematical Foundations of Computer Science (MFCS 2022)},
  pages =	{44:1--44:14},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-256-3},
  ISSN =	{1868-8969},
  year =	{2022},
  volume =	{241},
  editor =	{Szeider, Stefan and Ganian, Robert and Silva, Alexandra},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.MFCS.2022.44},
  URN =		{urn:nbn:de:0030-drops-168425},
  doi =		{10.4230/LIPIcs.MFCS.2022.44},
  annote =	{Keywords: monoidal categories, string diagrams, formal language theory, cartesian restriction categories}
}