 
Summary: Verifying Continuous Time Markov Chains
Adnan Aziz Kumud Sanwal Vigyan Singhal Robert Brayton
ECE Bell Labs CBL EECS
UT Austin AT&T Cadence UC Berkeley
Abstract. 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.
Introduction
Recent work on formal verification has addressed systems with stochastic dy
namics. Certain models for discrete time Markov chains have been investigated
in [6, 3]. However, a large class of stochastic systems operate in continuous time.
In a generalized decision and control framework, continuous time Markov chains
form a useful extension [9]. In this paper we propose a logic for specifying prop
erties of such systems, and describe a decision procedure for the model checking
problem. Our result differs from past work in this area [2] in that quantitative
bounds on the probability of events can be expressed in the logic.
1 Continuous Markov Chains
