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Presenting Convex Sets of Probability Distributions by Convex Semilattices and Unique Bases ((Co)algebraic pearls)

Authors Filippo Bonchi, Ana Sokolova, Valeria Vignudelli

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Author Details

Filippo Bonchi
  • University of Pisa, Italy
Ana Sokolova
  • University of Salzburg, Austria
Valeria Vignudelli
  • Univ Lyon, CNRS, ENS Lyon, UCB Lyon 1, LIP, France

Funding

  • Bonchi, Filippo: Supported by the Ministero dell’Università e della Ricerca of Italy under Grant No. 201784YSZ5, PRIN2017 – ASPRA (Analysis of Program Analyses).
  • Vignudelli, Valeria: Supported by the French projects ANR-20-CE48-0005 QuaReMe and ANR-16-CE25-0011 REPAS, the European Research Council (ERC) under the European Union’s Horizon 2020 programme (CoVeCe, grant agreement No 678157), the LABEX MILYON (ANR-10-LABX-0070) of Université de Lyon, within the program "Investissements d'Avenir" (ANR-11-IDEX-0007) operated by the French National Research Agency (ANR).

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Filippo Bonchi, Ana Sokolova, and Valeria Vignudelli. Presenting Convex Sets of Probability Distributions by Convex Semilattices and Unique Bases ((Co)algebraic pearls). In 9th Conference on Algebra and Coalgebra in Computer Science (CALCO 2021). Leibniz International Proceedings in Informatics (LIPIcs), Volume 211, pp. 11:1-11:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2021)
https://doi.org/10.4230/LIPIcs.CALCO.2021.11

Abstract

We prove that every finitely generated convex set of finitely supported probability distributions has a unique base. We apply this result to provide an alternative proof of a recent result: the algebraic theory of convex semilattices presents the monad of convex sets of probability distributions.

Subject Classification

ACM Subject Classification
  • Theory of computation → Logic and verification
  • Theory of computation → Axiomatic semantics
  • Theory of computation → Categorical semantics
Keywords
  • Convex sets of distributions monad
  • Convex semilattices
  • Unique base

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