# Approximate reasoning for real-time probabilistic processes

@article{Gupta2004ApproximateRF, title={Approximate reasoning for real-time probabilistic processes}, author={Vineet Gupta and Radha Jagadeesan and P. Panangaden}, journal={First International Conference on the Quantitative Evaluation of Systems, 2004. QEST 2004. Proceedings.}, year={2004}, pages={304-313} }

We develop a pseudo-metric analogue of bisimulation for generalized semiMarkov 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…

## 27 Citations

### Topologies of Stochastic Markov Models: Computational Aspects

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In this paper we propose two behavioral distances that support approximate reasoning on Stochastic Markov Models (SMMs), that are continuous-time stochastic transition systems where the residence…

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This work introduces a logical formalism for reasoning about upper and lower bounds on time, and studies the properties of this formalism, including axiomatisation and algorithms for checking when a formula is satisfied, and considers the question of when a system is faster than another system.

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### The Measurable Space of Stochastic Processes

- Mathematics, Computer Science2010 Seventh International Conference on the Quantitative Evaluation of Systems
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It is proved that stochastic bisimulation is a congruence that extends structural congruences and the calculus provides a canonic way to define metrics on processes that measure that measure how similar two processes are in terms of behaviour.

### A Behavioural Pseudometric for Metric Labelled Transition Systems

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In this paper a behavioural pseudometric is introduced for metric labelled transition systems, which generalise the fixed point, logical and coinductive characterisations of bisimilarity.

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