Trustworthy Systems

Characterising testing preorders for finite probabilistic processes


Yuxin Deng, Rob van Glabbeek, Matthew Hennessy and Carroll Morgan

Shanghai Jiao Tong University



University of Sussex


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.

BibTeX Entry

    author           = {Deng, Yuxin and van Glabbeek, Robert and Hennessy, Matthew and Morgan, Carroll},
    issn             = {1860-5974},
    journal          = {Logical Methods in Computer Science},
    keywords         = {probabilistic processes, nondeterminism, csp, transition systems, testing equivalences, simulation,
                        failure simulation, modal characterisations, complete axiomatisations.},
    month            = oct,
    number           = {4},
    pages            = {1--33},
    paperurl         = {},
    title            = {Characterising Testing Preorders for Finite Probabilistic Processes},
    volume           = {4},
    year             = {2008}