Probabilistic Analysis using Theorem Proving

Traditionally, computer simulation techniques are used to perform probabilistic analysis. However, they provide less accurate results and cannot handle large-scale problems due to their enormous CPU time requirements. Recently, a significant amount of formalization has been done in the HOL theorem prover that allows us to conduct precise probabilistic analysis using theorem proving and thus overcome the limitations of the simulation based probabilistic analysis approach. Some major contributions include the formalization of both discrete and continuous random variables and the verification of some of their corresponding probabilistic and statistical properties. This paper presents a concise description of the infrastructures behind these capabilities and the utilization of these features to conduct the probabilistic analysis of real-world systems. For illustration purposes, the paper describes the theorem proving based probabilistic analysis of three examples, i.e., the roundoff error of a digital processor, the Coupon Collector’s problem and the Stop-and-Wait protocol.