A Unifying Approach to Probabilistic Testing Equivalences

TL;DR

This paper introduces a unifying probabilistic testing framework for concurrent systems, providing new semantics, characterizations, and demonstrating its applicability through a case study on pCSP.

Contribution

It proposes a new distribution-based semantics and a generalized testing equivalence framework for probabilistic models, extending classical notions and ensuring they are congruences.

Findings

Characterization of testing equivalences via new semantics

Equivalences shown to be congruences

Case study on pCSP demonstrates framework flexibility

Abstract

Probabilistic concurrent systems are foundational models for modern mobile computing. In this paper, a unifying approach to probabilistic testing equivalences is proposed. With the help of a new distribution-based semantics for probabilistic models and a probabilistic testing framework with respect to process predicates, the internal characterization and the external characterization for testing equivalences are studied. The latter characterization can be viewed as the generalization of the classical fair/should equivalence and may equivalence. These equivalences are shown to be congruences. A thorough comparison between these equivalences and probabilistic bisimilarities is carried out. The techniques introduced in this paper can be easily extended to other probabilistic concurrent models. To showcase this flexibility, a case study is carried out on the pCSP model.