Gupta, Vineet and Jagadeesan, Radha and Panangaden, Prakash - Approximate reasoning for real-time probabilistic processes

lmcs:2258 - Logical Methods in Computer Science, March 7, 2006, Volume 2, Issue 1
Approximate reasoning for real-time probabilistic processes

Authors: Gupta, Vineet and Jagadeesan, Radha and Panangaden, Prakash

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 pseudo-metric gives a useful handle on approximate reasoning in the presence of numerical information -- such as probabilities and time -- in the model. 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. We show that several quantitative properties of interest are continuous with respect to the pseudo-metric. Thus, if two processes are metrically close, then observable quantitative properties of interest are indeed close.


Source : oai:arXiv.org:cs/0505063
DOI : 10.2168/LMCS-2(1:4)2006
Volume: Volume 2, Issue 1
Published on: March 7, 2006
Submitted on: November 21, 2016
Keywords: Computer Science - Logic in Computer Science,D.2.4,D.2.8,D.4.8,G.3


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