Model Checking Knowledge and Time

Model checking as an approach to the automatic veri cation of nite state systems has focussed predominantly on system speci cations expressed in temporal logic. In the distributed systems community, logics of knowledge (epistemic logics) have been advocated for expressing desirable properties of protocols and systems. A range of logics combining temporal and epistemic components have been developed for this purpose. However, the model checking problem for temporal logics of knowledge has received (comparatively) little attention. In this paper, we address ourselves to this problem. Following a brief survey of the relevant issues and literature, we introduce a temporal logic of knowledge (Halpern and Vardi's logic KLn ). We then develop an approach to KLn model checking that combines ideas from the interpreted systems semantics for knowledge with the logic of local propositions developed by Engelhardt et al. With our approach, KLn model checking can be reduced to linear temporal logic model checking. After introducing and exploring the ideas underpinning our approach, we present a case study (the bit transmission problem) in which spin was used to establish temporal epistemic properties of a system implemented in promela.