Summary: [Le90] H.R. Lewis, ``A logic of concrete time intervals,'' In Proceedings of the Fifth IEEE
Symposium on Logic in Computer Science, pages 380389, 1990.
[LS82] D. Lehman, S. Shelah, ``Reasoning with time and chance,'' Information and Con
trol 53, 1982.
[PZ86] A. Pnueli, L. Zuck, ``Probabilistic verification by tableaux,'' In Proceedings of the
First IEEE Symposium on Logic in Computer Science, 1986.
[Sh87] G.S. Shedler, Regeneration and Networks of Queues, SpringerVerlag, 1987.
[Th90] W. Thomas, ``Automata on infinite objects,'' Handbook of Theoretical Computer
Science, volume B, pages 133191, 1990.
[Wh80] W. Whitt, ``Continuity of generalized semiMarkov processes,'' Math. Oper. Res.
[Va85] M. Vardi, ``Automatic verification of probabilistic concurrent finitestate pro
grams,'' In Proceedings of the 26th IEEE Symposium on Foundations of Computer
Science, pages 327338, 1985.
fications. We do not yet know how to check properties specified using nondeterministic
timed automata or using linear realtime logics.
The algorithm outlined here is expensive. To make it more practical, some heuris
tic techniques need to be devised. Observe that the verification problems are typically
PSPACE, even in the absence of realtime and probabilities. We feel hopeful that the