Presenting convex sets of probability distributions by convex semilattices and unique bases

Filippo Bonchi (1) , Ana Sokolova (2) , Vignudelli Valeria (3, 4, 5, 6)

1 University of Pisa - Università di Pisa
2 University of Salzburg
3 ENS de Lyon - École normale supérieure de Lyon
4 CNRS - Centre National de la Recherche Scientifique
5 UCBL - Université Claude Bernard Lyon 1
6 LIP - Laboratoire de l'Informatique du Parallélisme

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.

Domaines: Logique en informatique [cs.LO]; Théorie et langage formel [cs.FL]

Filippo Bonchi, Ana Sokolova, Vignudelli Valeria. Presenting convex sets of probability distributions by convex semilattices and unique bases. 9th Conference on Algebra and Coalgebra in Computer Science (CALCO 2021), Aug 2021, Salzburg, Austria. ⟨10.4230/LIPIcs.CALCO.2021.11⟩. ⟨hal-03615765⟩