Trustworthy Systems

Characterising testing preorders for finite probabilistic processes


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

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

    address          = {Wroclaw, Poland},
    author           = {Deng, Yuxin and van Glabbeek, Robert and Hennessy, Matthew and Morgan, Carroll and Zhang, Cuicui},
    booktitle        = {Annual IEEE Symposium on Logic in Computer Science},
    isbn             = {978-0-7695-2908-0},
    keywords         = {probabilistic processes, nondeterminism, csp, transition systems, testing equivalences, simulation,
                        failure simulation, modal characterisations, complete axiomatisations.},
    month            = jul,
    pages            = {313--322},
    paperurl         = {},
    publisher        = {IEEE Computer Society Press},
    title            = {Characterising Testing Preorders for Finite Probabilistic Processes},
    year             = {2007}