A smooth probabilistic extension of concurrent constraint programming
Romain Beauxis · 2009
C constraint programming (CCP, [1]) is a model of computation in which the information available to the process is represented by the notion of constraint. Each process has access to a global store, with respect to which it tests and adds constraints. A domain-theoretic denotational semantics for CCP has been defined in [2]. In this semantics a process is mapped to the set of resting points that it can reach. It is possible to compute this set by a fixed point construction. This paper studies an extension of CCP with probabilistic executions. We develop a mathematical framework for defining the meaning of an infinite probabilistic execution. We use a topological notion of probability called the valuations, and give the conditions under which the limit of infinite executions exists and enjoys the expected properties. Using this result, we define a denotational semantics in which closure operators on constraints are replaced by linear closure operators on vector spaces.