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 higher-order logic§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 §corresponding probabilistic and statistical§properties. This book presents a concise description§of the infrastructures behind these capabilities and§their utilization to conduct the probabilistic§analysis of real-world systems. The case studies of§the round-off error of a digital processor, the§Coupon Collector's problem and the Stop-and-Wait§protocol are used to illustrate the proposed analysis§approach. §§Designed as an independent research tool, the book§presents a well-thought-out treatment of a rapidly§emerging multidisciplinary field across Mathematics,§Computer Science and Engineering. 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 higher-order logic§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 §corresponding probabilistic and statistical§properties. This book presents a concise description§of the infrastructures behind these capabilities and§their utilization to conduct the probabilistic§analysis of real-world systems. The case studies of§the round-off error of a digital processor, the§Coupon Collector''s problem and the Stop-and-Wait§protocol are used to illustrate the proposed analysis§approach. §Designed as an independent research tool, the book§presents a well-thought-out treatment of a rapidly§emerging multidisciplinary field across Mathematics,§Computer Science and Engineering.