Restricted Congruences In Computing
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Restricted Congruences in Computing
Congruences are ubiquitous in computer science, engineering, mathematics, and related areas. Developing techniques for finding (the number of) solutions of congruences is an important problem. But there are many scenarios in which we are interested in only a subset of the solutions; in other words, there are some restrictions. What do we know about these restricted congruences, their solutions, and applications? This book introduces the tools that are needed when working on restricted congruences and then systematically studies a variety of restricted congruences. Restricted Congruences in Computing defines several types of restricted congruence, obtains explicit formulae for the number of their solutions using a wide range of tools and techniques, and discusses their applications in cryptography, information security, information theory, coding theory, string theory, quantum field theory, parallel computing, artificial intelligence, computational biology, discrete mathematics, number theory, and more. This is the first book devoted to restricted congruences and their applications. It will be of interest to graduate students and researchers across computer science, electrical engineering, and mathematics.
Measurement, Modeling, and Evaluation of Computing Systems and Dependability and Fault Tolerance
Author: Jens B. Schmitt
language: en
Publisher: Springer Science & Business Media
Release Date: 2012-03-09
This book constitutes the refereed proceedings of the 16th International GI/ITG Conference on Measurement, Modeling and Evaluation of Computing Systems and Dependability and Fault Tolerance, MMB & DFT 2012, held in Kaiserslautern, Germany, in March 2012. The 16 revised full papers presented together with 5 tool papers and 5 selected workshop papers were carefully reviewed and selected from 54 submissions. MMB & DFT 2012 covers diverse aspects of performance and dependability evaluation of systems including networks, computer architectures, distributed systems, software, fault-tolerant and secure systems.
Universal Algebra and Applications in Theoretical Computer Science
Over the past 20 years, the emergence of clone theory, hyperequational theory, commutator theory and tame congruence theory has led to a growth of universal algebra both in richness and in applications, especially in computer science. Yet most of the classic books on the subject are long out of print and, to date, no other book has integrated these theories with the long-established work that supports them. Universal Algebra and Applications in Theoretical Computer Science introduces the basic concepts of universal algebra and surveys some of the newer developments in the field. The first half of the book provides a solid grounding in the core material. A leisurely pace, careful exposition, numerous examples, and exercises combine to form an introduction to the subject ideal for beginning graduate students or researchers from other areas. The second half of the book focuses on applications in theoretical computer science and advanced topics, including Mal'cev conditions, tame congruence theory, clones, and commutators. The impact of the advances in universal algebra on computer science is just beginning to be realized, and the field will undoubtedly continue to grow and mature. Universal Algebra and Applications in Theoretical Computer Science forms an outstanding text and offers a unique opportunity to build the foundation needed for further developments in its theory and in its computer science applications.