Approximate reasoning for realtime probabilistic processes
Abstract
We develop a pseudometric analogue of bisimulation for generalized semiMarkov processes. The kernel of this pseudometric corresponds to bisimulation; thus we have extended bisimulation for continuoustime 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. We give a fixed point characterization of the pseudometric. 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 realvalued modal logic. 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.
 Publication:

arXiv eprints
 Pub Date:
 May 2005
 arXiv:
 arXiv:cs/0505063
 Bibcode:
 2005cs........5063G
 Keywords:

 Computer Science  Logic in Computer Science;
 D.2.4;
 D.2.8;
 D.4.8;
 G.3
 EPrint:
 Preliminary version appeared in QEST 04