Restricted Congruences in Computing
“Restricted Congruences in Computing” by Khodakhast Bibak, published by Taylor & Francis Group on April 22, 2022, is a comprehensive exploration of restricted congruences and their applications across various fields. This 145-page book presents essential techniques for finding solutions to congruences, focusing on scenarios where only specific subsets of solutions are relevant. The text provides a systematic study of different types of restricted congruences, offering explicit formulae for their solutions and discussing their significance in areas such as cryptography, information security, and artificial intelligence.
Readers will find a detailed introduction to the tools necessary for working with restricted congruences, along with an examination of their applications in diverse disciplines, including computer science, mathematics, and engineering. The book emphasizes the relevance of restricted congruences in mathematical and statistical software, game theory, and optical data processing. As the first dedicated work on this topic, it serves as a valuable resource for graduate students and researchers seeking to deepen their understanding of restricted congruences and their practical implications.
Official synopsis Publisher
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.
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