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Real-Reward Testing for Probabilistic Processes (Extended Abstract)

Author(s): Yuxin Deng | Rob van Glabbeek | Matthew Hennessy | Carroll Morgan

Journal: Electronic Proceedings in Theoretical Computer Science
ISSN 2075-2180

Volume: 57;
Issue: Proc. QAPL 2011;
Start page: 61;
Date: 2011;
Original page

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.
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