Characterising Testing Preorders for Finite Probabilistic Processes

TL;DR

This paper provides complete axiomatizations and characterizations of may and must testing preorders for finite probabilistic processes, using simulation, failure simulation, modal logic, and CSP extensions.

Contribution

It offers the first complete axiomatizations and characterizations of these preorders for finite probabilistic processes with silent moves.

Findings

May preorder characterised by simulation.

Must preorder characterised by failure simulation.

Modal logic characterizations provided.

Abstract

In 1992 Wang & Larsen extended the may- and must preorders of De Nicola and Hennessy to processes featuring probabilistic as well as nondeterministic choice. They concluded with two problems that have remained open throughout the years, namely to find complete axiomatisations and alternative characterisations for these preorders. This paper solves both problems for finite processes with silent moves. It characterises the may preorder in terms of simulation, and the must preorder in terms of failure simulation. It also gives a characterisation of both preorders using a modal logic. Finally it axiomatises both preorders over a probabilistic version of CSP.