Aspects of probabilistic process algebra

We introduce probability into classical process algebra and investigate the impact of this addition on process equivalence and its axiomatization. We begin by extending Milner's Synchronous Calculus of Communicating Systems (SCCS) to obtain PCCS, a language for communicating probabilistic processes. Plotkin-style structural operational semantics of the language is then defined. We present an application of PCCS involving the modeling and performance analysis of the AUY communicating protocol for deletion errors. Our study of process equivalence begins with the definition of trace, maximal trace, failure, maximal failure, ready, and bisimulation equivalence of probabilistic labeled transition systems, our model for probabilistic processes. We show that, unlike nondeterministic transition systems, "maximality" of traces and failures does not increase the distinguishing power of trace and failure equivalence, respectively. Thus, in the probabilistic case, trace and maximal trace equivalence coincide, and failure and ready equivalence coincide. We then show that of trace, failure, and bisimulation equivalence, only the last is a congruence with respect to PCCS. Trace and ready equivalence are, however, congruences with respect to restriction-free PCCS. Probabilistic bisimulation is weakened to obtain a family of probabilistic similarity relations on processes, in which processes simulate each other within a bound $\epsilon$ of deviation in probability. Probabilistic similarity in turn gives rise to a distance function on processes. We show that this distance function and the set of processes whose underlying transition structure is deterministic form a metric space, and in most PCCS contexts the effect of expression replacement on distance is either contractional or isometric. A simple algebraic analysis of faulty multi-bit pipelines is given to illustrate the utility of the metric space. We then present sound and complete axiomatizations of probabilistic bisimulation for finite and finite-state probabilistic processes. Of particular interest in the finite-state case is the rule for eliminating unguarded recursion, which characterizes the possibility of infinite syntactic substitution as a zero-probability event. Finally, we extend our model of probabilistic processes to allow internal actions. We define a probabilistic extension of Van Glabbeek and Weijland's branching bisimulation, and completely axiomatize probabilistic branching bisimulation for finite probabilistic processes with internal actions.