Combining probabilistic and non-deterministic choice via weak distributive laws

Alexandre Goy (1) , Daniela Petrişan (2)

1 MICS - Mathématiques et Informatique pour la Complexité et les Systèmes
2 IRIF (UMR_8243) - Institut de Recherche en Informatique Fondamentale

Combining probabilistic choice and non-determinism is a long standing problem in denotational semantics. From a category theory perspective, the problem stems from the absence of a distributive law of the powerset monad over the distribution monad. In this paper we prove the existence of a weak distributive law of the powerset monad over the finite distribution monad. As a consequence, we retrieve the well-known convex powerset monad as a weak lifting of the powerset monad to the category of convex algebras. We provide applications to the study of trace semantics and behavioral equivalences of systems with an interplay between probability and non-determinism.

Mots clés: weak distributive law; weak lifting; finite distribution monad; convex powerset monad; trace semantics; behavioral equivalence; probability; non-determinism; probabilistic automata

Domaines: Informatique [cs]; Logique en informatique [cs.LO]

Alexandre Goy, Daniela Petrişan. Combining probabilistic and non-deterministic choice via weak distributive laws. LICS '20: Proceedings of the 35th Annual ACM/IEEE Symposium on Logic in Computer Science, Jul 2020, Saarbrücken, Germany. pp.454-464, ⟨10.1145/3373718.3394795⟩. ⟨hal-02564365⟩