Applications of Continuous Mathematics to Computer Science

Description

This volume is intended to be used as a textbook for a special topic course in computer science. It addresses contemporary research topics of interest such as intelligent control, genetic algorithms, neural networks, optimization techniques, expert systems, fractals, and computer vision. The work incorporates many new research ideas, and focuses on the role of continuous mathematics. Audience: This book will be valuable to graduate students interested in theoretical computer topics, algorithms, expert systems, neural networks, and software engineering. Front Matter ....Pages i-xii Algorithm Complexity: Two Simple Examples (Hung T. Nguyen, Vladik Kreinovich)....Pages 1-20 Solving General Linear Functional Equations: an Application to Algorithm Complexity (Hung T. Nguyen, Vladik Kreinovich)....Pages 21-44 Program Testing: A Problem (Hung T. Nguyen, Vladik Kreinovich)....Pages 45-64 Optimal Program Testing (Hung T. Nguyen, Vladik Kreinovich)....Pages 65-86 Optimal Choice of a Penalty Function: Simplest Case of Algorithm Design (Hung T. Nguyen, Vladik Kreinovich)....Pages 87-107 Solving General Linear Differential Equations with Constant Coefficients: An Application to Constrained Optimization (Hung T. Nguyen, Vladik Kreinovich)....Pages 109-129 Simulated Annealing: “Smooth” (Local) Discrete Optimization (Hung T. Nguyen, Vladik Kreinovich)....Pages 131-152 Genetic Algorithms:“Non-Smooth” Discrete Optimization (Hung T. Nguyen, Vladik Kreinovich)....Pages 153-173 RISC Computer Architecture and Internet Growth: Two Applications of Extrapolation (Hung T. Nguyen, Vladik Kreinovich)....Pages 175-195 Systems of Differential Equations and Their Use in Computer-Related Extrapolation Problems (Hung T. Nguyen, Vladik Kreinovich)....Pages 197-223 Network Congestion: An Example of Non-Linear Extrapolation (Hung T. Nguyen, Vladik Kreinovich)....Pages 225-250 Neural Networks: A General form of Non-Linear Extrapolation (Hung T. Nguyen, Vladik Kreinovich)....Pages 251-274 Expert Systems and the Basics of Fuzzy Logic (Hung T. Nguyen, Vladik Kreinovich)....Pages 275-296 Intelligent and Fuzzy Control (Hung T. Nguyen, Vladik Kreinovich)....Pages 297-322 Randomness, Chaos, and Fractals (Hung T. Nguyen, Vladik Kreinovich)....Pages 323-350 Back Matter ....Pages 351-419