Continuous Random Variables

Jean Goubault-Larrecq (1, 2) , Daniele Varacca (3)

1 LSV - Laboratoire Spécification et Vérification [Cachan]
2 SECSI - Security of information systems
3 PPS - Preuves, Programmes et Systèmes

We introduce the domain of continuous random variables (CRV) over a domain, as an alternative to Jones and Plotkin's probabilistic power domain. While no known Cartesian-closed category is stable under the latter, we show that the so-called thin (uniform) CRVs define a strong monad on the Cartesian-closed category of bc-domains. We also characterize their inequational theory, as (fair-)coin algebras. We apply this to solve a recent problem posed by M. Escardo: testing is semi-decidable for EPCF terms. CRVs arose from the study of the second author's (layered) Hoare indexed valuations, and we also make the connection apparent.

Domaines: Théorie et langage formel [cs.FL]

Jean Goubault-Larrecq, Daniele Varacca. Continuous Random Variables. IEEE symposium of Logic In Computer Science, Jun 2011, Toronto, Canada. pp.97-106. ⟨hal-00629723⟩