Axiomatizing probabilistic processes: ACP with generative probabilities

AbstractThis paper is concerned with finding complete axiomatizations of probabilistic processes. We examine this problem within the context of the process algebra ACP and obtain as our endresult the axiom system pr ACP−l, a version of ACP whose main innovation is a probabilistic asynchronous interleaving operator. Our goal was to introduce probability into ACP in as simple a fashion as possible, Optimally, ACP should be the homomorphic image of the probabilistic version in which the probabilities are forgotten, We begin by weakening slightly ACP to obtain the axiom system ACP−l. The main difference between ACP and ACP−l is that the axiom x + δ = x, which does not yield a plausible interpretation in the generative model of probabilistic computation, is rejected in ACP−l. We argue that this does not affect the usefulness of ACP−l in practice, and show how ACP can be reconstructed from ACP−l with a minimal amount of technical machinery. pr ACP−l is obtained from ACP−l through the introduction of probabilistic alternative and parallel composition operators, and a process graph model for pr ACP−l based on probabilistic bisimulation is developed. We show that pr ACP−l is a sound and complete axiomatization of probabilistic bisimulation for finite processes, and that pr ACP−l can be homomorphically embedded in ACP−l as desired. Our results for ACP−l and pr ACP−l are presented in a modular fashion by first considering several subsets of the signatures, We conclude with a discussion about adding an iteration operator to pr ACP−l

Efficient property preservation checking of model refinements

In model-driven software development, models and model refinements are used to create software. To automatically generate correct software from abstract models by means of model refinement, desirable properties of the initial models must be preserved. We propose an explicit-state model checking technique to determine whether refinements are property preserving. We use networks of labelled transition systems (LTSs) to represent models with concurrent components, and formalise refinements as systems of LTS transformation rules. Property preservation checking involves determining how a rule system relates to an input network, and checking bisimilarity between behaviour subjected to transformation and the corresponding behaviour after transformation. In this way, one avoids generating the entire LTS of the new model. Experimental results demonstrate speedups of several orders of magnitude