Polynomial systems are fundamental tools in the solution of hard problems in science and engineering such as robotics, automated reasoning, artificial intelligence and signal processing. Similarly, from the early days of the digital era, Boolean variables have been the foundations of the computer operations. Hence, the application of common algebraic techniques to Boolean algebra is used now as a method to solve complex Boolean equation systems that before were only intended to solve using Boolean logic techniques. The aim of this project is to demonstrate that Zhegalkin polynomials (also known as Algebraic Normal Form - ANF) are an alternative way to represent Boolean functions. In order to test the hypothesis, a Zhegalkin SAT Solver (ZPSAT) was developed. The results conducted after the testing concluded that ZPSAT can solve a conjunction of XOR equations efficiently in terms of reliability and computing time. The heuristic used to build ZPSAT was based mainly on the concepts used by the Horn Formulae and a Fast-Multiplication method of two ANF polynomials known as Mobius transform.
This textbook presents fundamental machine learning concepts in an easy to understand manner by providing practical advice, using straightforward examples, and offering engaging discussions of relevant applications. The main topics include Bayesian classifiers, nearest-neighbor classifiers, linear and polynomial classifiers, decision trees, neural networks, and support vector machines. Later chapters show how to combine these simple tools by way of ´´boosting,´´ how to exploit them in more complicated domains, and how to deal with diverse advanced practical issues. One chapter is dedicated to the popular genetic algorithms. This revised edition contains three entirely new chapters on critical topics regarding the pragmatic application of machine learning in industry. The chapters examine multi-label domains, unsupervised learning and its use in deep learning, and logical approaches to induction. Numerous chapters have been expanded, and the presentation of the material has been enhanced. The book contains many new exercises, numerous solved examples, thought-provoking experiments, and computer assignments for independent work.