Testing Probabilistic and Nondeterministic Processes

Abstract In this paper, we extend Milner's CCS with a binary stochastic choice operator, ⊕p indexed with a probability p ∈]0, 1[to model probabilistic and nondeterministic processes. Intuitively, P ⊕p Q may move to P immediately with probability p, written P ⊗ p Q ⟶ e p P , , or to Q with probability 1 – p. Based on de Nicola and Hennessy's testing [NH84], a theory of testing is proposed. Given a process P and a test T, we define a notion of P can pass T with a set of probabilities φ(P,T). For non-probabilistic processes and tests (e.g. written in CCS), it turns out that P must satisfy T when inf{φ(P,T)} = 1 and P may satisfy T when sup{φ(P,T)} = 1, where may satisfy and must satisfy are the two satisfaction relations between processes and tests due to de Nicola and Hennessy. In terms of φ(P,T), three testing preorders are defined, which in turn generalize Nicola-Hennessy's may, must and test preorders to probabilistic and nondeterministic processes. Finally, as an example, a simple communication protocol is described and proved to behave like a one-place buffer.

[1]  Rocco De Nicola,et al.  Testing Equivalences for Processes , 1984, Theor. Comput. Sci..

[2]  Robin Milner,et al.  A Calculus of Communicating Systems , 1980, Lecture Notes in Computer Science.

[3]  Bengt Jonsson,et al.  A calculus for communicating systems with time and probabilities , 1990, [1990] Proceedings 11th Real-Time Systems Symposium.