Discrete Random Variables over Domains

In this paper we initiate the study of discrete random variables over domains. Our work is inspired by work of Daniele Varacca, who devised indexed valuations as models of probabilistic computation within domain theory. Our approach relies on new results about commutative monoids defined on domains that also allow actions of the non-negative reals. Using our approach, we define two such families of real domain monoids, one of which allows us to recapture Varacca’s construction of the Plotkin indexed valuations over a domain. Each of these families leads to the construction of a family of discrete random variables over domains, the second of which forms the object level of a continuous endofunctor on the categories RB (domains that are retracts of bifinite domains), and on FS (domains where the identity map is the directed supremum of deflations finitely separated from the identity). The significance of this last result lies in the fact that there is no known category of contin...

• Type: Conference
• Year: 2005
• Where: ICALP
• Authors: Michael W. Mislove
• Keywords: Discrete Random Variables, ICALP 2005, Indexed Valuations, Probabilistic, Theoretical Computer Science