A Markov Model for Probabilistic Concurrent Constraint Programming

This paper introduces a new approach towards the semantics of Concurrent Constraint Programming (CCP), which is based on operator algebras. In particular , we show how stochastic matrices can be used for modelling both a quantitative version of nondeterminism (in the form of a probabilistic choice) and synchronisa-tion. We will assume Probabilistic Concurrent Constraint Programming (PCCP) as the reference paradigm. The presented model subsumes CCP as a special case. The model is obtained by a xpoint construction on a space of linear operators. For the purpose of this paper, we consider only nite constraint systems. This allows us to deene our model by using nite dimensional linear operators, i.e. matrices. We show that our model is equivalent to a notion of observables which extends the standard one in CCP (input/output behaviour) by including information about the likelihood of the computed results. The model also captures innnite computations.