Scientists and engineers often have to deal with systems that exhibit random or unpredictable elements and must effectively evaluate probabilities in each situation. Computer simulations, while the traditional tool used to solve such problems, are limited in the scale and complexity of the problems they can solve. Formalized Probability Theory and Applications Using Theorem Proving discusses some of the limitations inherent in computer systems when applied to problems of probabilistic analysis, and presents a novel solution to these limitations, combining higher-order logic with computer-based theorem proving. Combining practical application with theoretical discussion, this book is an important reference tool for mathematicians, scientists, engineers, and researchers in all STEM fields.

This book describes an accurate analysis technique for energy systems based on formal methods-computer-based mathematical logic techniques for the specification, validation, and verification of the systems. Correctness and accuracy of the financial, operational, and implementation analysis are of the paramount importance for the materialization of the future energy systems, such as smart grids, to achieve the objectives of cost-effectiveness, efficiency, and quality-of-service. In this regard, the book develops formal theories of microeconomics, asymptotic, and stability to support the formal analysis of generation and distribution cost, smart operations, and processing of energy in a smart grid. These formal theories are also employed to formally verify the cost and utility modeling for: Energy generation and distribution; Asymptotic bounds for online scheduling algorithms for plug-in electric vehicles; and Stability of the power converters for wind turbines. The proposed approach results in mechanized proofs for the specification, validation, and verification of corresponding smart grid problems. The formal mathematical theories developed can be applied to the formal analysis of several other hardware and software systems as well, making this book of interest to researchers and practicing engineers in a variety of power electronic fields.

This book constitutes the refereed proceedings of the 10th International Conference on Intelligent Computer Mathematics, CICM 2017, held in Edinburgh, Scotland, in July 2017. The 22 full papers and 3 abstracts of invited papers presented were carefully reviewed and selected from a total of 40 submissions. The papers are organized in three tracks: the Calculemus track examining the integration of symbolic computation and mechanized reasoning; the Digital Mathematics Libraries track dealing with math-aware technologies, standards, algorithms, and processes; the Mathematical Knowledge Management track being concerned with all aspects of managing mathematical knowledge, in informal, semi-formal, and formal settings. An additional track Systems and Projects contains descriptions of systems and relevant projects, both of which are key to a research topic where theory and practice interact on explicitly represented knowledge.

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.