@article{cleaveland_iyer_narasimha_2005, title={Probabilistic temporal logics via the modal mu-calculus}, volume={342}, ISSN={["1879-2294"]}, DOI={10.1016/j.tcs.2005.03.048}, abstractNote={This paper presents a mu-calculus-based modal logic for describing properties of reactive probabilistic labeled transition systems (RPLTSs) and develops a model-checking algorithm for determining whether or not states in finite-state RPLTSs satisfy formulas in the logic. The logic is based on the distinction between (probabilistic) “systems” and (nonprobabilistic) “observations”: using the modal mu-calculus, one may specify sets of observations, and the semantics of our logic then enable statements to be made about the measures of such sets at various system states. The logic may be used to encode a variety of probabilistic modal and temporal logics; in addition, the model-checking problem for it may be reduced to the calculation of solutions to systems of non-linear equations. Finally, the logic induces an equivalence on RPLTSs that coincides with accepted notions of probabilistic bisimulation in the literature.}, number={2-3}, journal={THEORETICAL COMPUTER SCIENCE}, author={Cleaveland, R and Iyer, SP and Narasimha, M}, year={2005}, month={Sep}, pages={316–350} }
 @inbook{narasimha_cleaveland_iyer_1999, title={Probabilistic temporal logics via the modal mu-calculus}, volume={1578}, ISBN={3540657193}, booktitle={Foundations of software science and computation structures: Second International Conference, FOSSACS '99 held as part of the joint European Conferences on Theory and Practice of Software, ETAPS'99, Amsterdam, The Netherlands, March 22-28, 1999: proceedings}, publisher={Berlin; New York: Springer}, author={Narasimha, M. and Cleaveland, R. and Iyer, P.}, year={1999}, pages={288–305} }