Algebraic theory of probabilistic processes

In this paper we extend de Nicola and Hennessy’s testing theory to deal with probabilities. We say that two processes are testing equivalent if the probabilities with which they pass any test are equal. We present three alternative semantic views of our testing equivalence. First, we introduce adequate extensions of acceptance sets (inducing an operational characterization) and acceptance trees (inducing a denotational semantics). We also present a sound and complete axiomatization of our testing equivalence. So, this paper represents a complete study of the adaptation of the classical testing theory for probabilistic processes.