Formalization of Birth-Death and IID processes in higher-order logic

摘要

Markov chains are extensively used in the modeling and analysis of engineering and scientific problems. Usually, paper-and-pencil proofs, simulation or computer algebra software are used to analyze Markovian models. However, these techniques either are not scalable or do not guarantee accurate results, which are vital in safety-critical systems. Probabilistic model checking has been proposed to formally analyze Markovian systems, but it suffers from the inherent state-explosion problem and unacceptable long computation times. Higher-order-logic theorem proving has been recently used to overcome the above-mentioned limitations but it lacks any support for discrete Birth-Death process and Independent and Identically Distributed (IID) random process, which are frequently used in many system analysis problems. In this paper, we formalize these notions using formal Discrete-Time Markov Chains (DTMC) with finite state-space and classified DTMCs in higher-order logic theorem proving. To demonstrate the usefulness of the formalizations, we present the formal performance analysis of two software applications.