A logic for reasoning about time and reliability

We present a logic for stating properties such as, "after a request for service there is at least a 98\045 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 satis- fies a formula in the logic. The algorithms require a polynomial number of arithmetic operations, in size of both the formula and\003This research report is a revised and extended version of a paper that has appeared under the title "A Framework for Reasoning about Time and Reliability" in the Proceeding of the 10thIEEE Real-time Systems Symposium, Santa Monica CA, December 1989. This work was partially supported by the Swedish Board for Technical Development (STU) as part of Esprit BRA Project SPEC, and by the Swedish Telecommunication Administration.1the Markov chain. A simple example is included to illustrate the algorithms.Original report number R90013.