We present a logical formalism for expressing properties of continuous time Markov chains. The semantics for such properties arise as a natural extension of previous work on discrete time Markov chains to continuous time. The major result is that the verification problem is decidable; this is shown using results in algebraic and transcendental number theory.

We present a logical formalism for expressing properties of continuous time Markov chains. The semantics for such properties arise as a natural extension of previous work on discrete time Markov chains to continuous time. The major result is that the verification problem is decidable; this is shown using results in algebraic and transcendental number gheory.

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In this paper the branching time logic pCTL* is defined.pCTL* expresses quantitative bounds on the probabilities of correct behavior; it can be interpreted over discrete Markov processes. A bisimulation relation is defined on finite Markov processes, and shown to be sound and complete with respect to pCTL*. We extend the universe of models to generalized Markov processes in order to support notions of refinement, abstraction, and parametrization. Model checking pCTL* over generalized Markov processes is shown to be elementary by a reduction to RCF. We conclude by describing practical and theoretical avenues for further work.

The logic of equality with uninterpreted functions has been proposed for verifying abstract hardware designs. The ability to perform fast satisfiability checking over this logic is imperative for this verification l)aradigm to be successfld. We present symbolic methods for satisfiability checking for this logic. The first procedure is based on restricting analysis to finite instantiations of the (lesign. The second procedure directly reasons about equality by introducing Boolean-valued indicator variables for equality. Theoretical and experimental evidence shows the superiority of tim second approach.