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Real reward testing for probabilistic processes

Authors

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

Shanghai Jiao Tong University

NICTA

UNSW

Trinity College Dublin

Abstract

We introduce a notion of real-valued reward testing for probabilistic processes by extending the traditional nonnegative-reward testing with negative rewards. In this richer testing framework, the may- and must preorders turn out to be inverses. We show that for convergent processes with finitely many states and transitions, but not in the presence of divergence, the real-reward must-testing preorder coincides with the nonnegative-reward must-testing preorder. To prove this coincidence we characterise the usual resolution-based testing in terms of the weak transitions of processes, without having to involve policies, adversaries, schedulers, resolutions or similar structures that are external to the process under investigation. This requires establishing the continuity of our function for calculating testing outcomes.

BibTeX Entry

  @article{Deng_GHM_14,
    doi              = {10.1016/j.tcs.2013.07.016},
    journal          = {Theoretical Computer Science},
    author           = {Deng, Yuxin and van Glabbeek, Robert and Hennessy, Matthew and Morgan, Carroll},
    month            = {jul},
    volume           = {538},
    year             = {2014},
    keywords         = {probabilistic processes, nondeterminism, transition systems, testing equivalences, reward testing,
                        failure simulation, divergence.},
    title            = {Real Reward Testing for Probabilistic Processes},
    pages            = {16-36}
  }

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