Formal Reasoning about Classified Markov Chains in HOL

Classified Markov chains have been extensively applied to model and analyze various stochastic systems in many engineering and scientific domains. Traditionally, the analysis of these systems has been conducted using computer simulations and, more recently, also probabilistic model-checking. However, these methods either cannot guarantee accurate analysis or are not scalable due to the unacceptable computation times. As an alternative approach, this paper proposes to reason about classified Markov chains using HOL theorem proving. We provide a formalization of classified discrete-time Markov chains with finite state space in higher-order logic and the formal verification of some of their widely used properties. To illustrate the usefulness of the proposed approach, we present the formal analysis of a generic LRU (least recently used) stack model.