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DOI: 10.4230/LIPIcs.CONCUR.2026.21

Completeness for Probabilistic Boolean Tapes

Authors: Filippo Bonchi and Cipriano Junior Cioffo

Published in: LIPIcs, Volume 391, 37th International Conference on Concurrency Theory (CONCUR 2026)

Abstract

Probabilistic Boolean circuits have recently been proposed as a string-diagrammatic foundation for finite probabilistic programming. In this paper, we present a complete set of axioms for their semantics in terms of Markov kernels. Our approach is based on two intermediate results: completeness for partial Boolean circuits and completeness for probabilistic Boolean tapes, a diagrammatic language for rig categories.

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Filippo Bonchi and Cipriano Junior Cioffo. Completeness for Probabilistic Boolean Tapes. In 37th International Conference on Concurrency Theory (CONCUR 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 391, pp. 21:1-21:23, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)

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@InProceedings{bonchi_et_al:LIPIcs.CONCUR.2026.21,
  author =	{Bonchi, Filippo and Cioffo, Cipriano Junior},
  title =	{{Completeness for Probabilistic Boolean Tapes}},
  booktitle =	{37th International Conference on Concurrency Theory (CONCUR 2026)},
  pages =	{21:1--21:23},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-447-5},
  ISSN =	{1868-8969},
  year =	{2026},
  volume =	{391},
  editor =	{Sokolova, Ana and Totzke, Patrick},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.CONCUR.2026.21},
  URN =		{urn:nbn:de:0030-drops-273525},
  doi =		{10.4230/LIPIcs.CONCUR.2026.21},
  annote =	{Keywords: String diagrams, Rig categories, synthetic probability theory}
}

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DOI: 10.4230/LIPIcs.CALCO.2025.11

Tape Diagrams for Monoidal Monads

Authors: Filippo Bonchi, Cipriano Junior Cioffo, Alessandro Di Giorgio, and Elena Di Lavore

Published in: LIPIcs, Volume 342, 11th Conference on Algebra and Coalgebra in Computer Science (CALCO 2025)

Abstract

Tape diagrams provide a graphical representation for arrows of rig categories, namely categories equipped with two monoidal structures, ⊕ and ⊗, where ⊗ distributes over ⊕. However, their applicability is limited to categories where ⊕ is a biproduct, i.e., both a categorical product and a coproduct. In this work, we extend tape diagrams to deal with Kleisli categories of symmetric monoidal monads, presented by algebraic theories.

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Filippo Bonchi, Cipriano Junior Cioffo, Alessandro Di Giorgio, and Elena Di Lavore. Tape Diagrams for Monoidal Monads. In 11th Conference on Algebra and Coalgebra in Computer Science (CALCO 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 342, pp. 11:1-11:24, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{bonchi_et_al:LIPIcs.CALCO.2025.11,
  author =	{Bonchi, Filippo and Cioffo, Cipriano Junior and Di Giorgio, Alessandro and Di Lavore, Elena},
  title =	{{Tape Diagrams for Monoidal Monads}},
  booktitle =	{11th Conference on Algebra and Coalgebra in Computer Science (CALCO 2025)},
  pages =	{11:1--11:24},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-383-6},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{342},
  editor =	{C\^{i}rstea, Corina and Knapp, Alexander},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.CALCO.2025.11},
  URN =		{urn:nbn:de:0030-drops-235703},
  doi =		{10.4230/LIPIcs.CALCO.2025.11},
  annote =	{Keywords: rig categories, string diagrams, monads, probabilistic control}
}

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Documents authored by Cioffo, Cipriano Junior

Completeness for Probabilistic Boolean Tapes

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Tape Diagrams for Monoidal Monads

Abstract

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