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A logic for reasoning about time and reliability

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Formal Aspects of Computing

Abstract

We present a logic for stating properties such as, “after a request for service there is at least a 98% probability that the service will be carried out within 2 seconds”. The logic extends the temporal logic CTL by Emerson, Clarke and Sistla with time and probabilities. Formulas are interpreted over discrete time Markov chains. We give algorithms for checking that a given Markov chain satisfies a formula in the logic. The algorithms require a polynomial number of arithmetic operations, in size of both the formula and the Markov chain. A simple example is included to illustrate the algorithms.

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  1. Department of Computer Systems, Uppsala University, Box 325, S-751 05, Uppsala, Sweden

    Hans Hansson & Bengt Jonsson

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  1. Hans Hansson
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Correspondence to Hans Hansson.

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Hansson, H., Jonsson, B. A logic for reasoning about time and reliability. Formal Aspects of Computing 6, 512–535 (1994). https://doi.org/10.1007/BF01211866

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