Quantitative Evaluation of Systems, International Conference on (2004)

Enschede, the Netherlands

Sept. 27, 2004 to Sept. 30, 2004

ISBN: 0-7695-2185-1

pp: 304-313

Vineet Gupta , Google Inc.

Radha Jagadeesan , DePaul University

Prakash Panangaden , McGill University

ABSTRACT

We develop a pseudo-metric analogue of bisimulation for generalized semi-Markov processes. The kernel of this pseudo-metric corresponds to bisimulation; thus we have extended bisimulation for continuous-time probabilistic processes to a much broader class of distributions than exponential distributions. This pseudometric gives a useful handle on approximate reasoning in the presence of numerical information - such as probabilities and time - in the model.<div></div> We give a fixed point characterization of the pseudo-metric. This makes available coinductive reasoning principles for reasoning about distances. We demonstrate that our approach is insensitive to potentially ad hoc articulations of distance by showing that it is intrinsic to an underlying uniformity. We provide a logical characterization of this uniformity using a real-valued modal logic.<div></div> We show that several quantitative properties of interest are continuous with respect to the pseudometric. Thus, if two processes are metrically close, then observable quantitative properties of interest are indeed close.

INDEX TERMS

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CITATION

P. Panangaden, V. Gupta and R. Jagadeesan, "Approximate Reasoning for Real-Time Probabilistic Processes,"

*Quantitative Evaluation of Systems, International Conference on(QEST)*, Enschede, the Netherlands, 2004, pp. 304-313.

doi:10.1109/QEST.2004.10029

CITATIONS