An operational semantics for probabilistic concurrent constraint programming

The paper investigates a probabilistic version of the concurrent constraint programming paradigm (CCP). The aim is to introduce the possibility to formulate so called "randomised algorithms" within the CCP framework. Differently from common approaches in (imperative) high level programming languages, which rely on some kind of random() function, we introduce randomness in the very definition of the language by means of a probabilistic choice construct. This allows a program to make stochastic moves during its execution. We call the resulting language probabilistic concurrent constraint programming (PCCP). We present an operational semantics for PCCP by means of a probabilistic transition system such that the execution of a PCCP program may be seen as a stochastic process, i.e. as a random walk on the transition graph. The transition probabilities are given explicitly. This semantics captures a notion of observables which combines results of computations and the probability of those results being computed. This embedding of randomness within the semantics of a well structured programming paradigm, like CCP, also aims at providing a sound framework for formalising and reasoning about randomised algorithms and programs. Additionally, we give some examples of PCCP programs and we show how well known randomised algorithms can be implemented very naturally in the new language.