Boolean Models And Methods In Mathematics Computer Science And Engineering

A collection of papers written by prominent experts that examine a variety of advanced topics related to Boolean functions and expressions.

Written by prominent experts in the field, this monograph provides the first comprehensive, unified presentation of the structural, algorithmic and applied aspects of the theory of Boolean functions. The book focuses on algebraic representations of Boolean functions, especially disjunctive and conjunctive normal form representations. This framework looks at the fundamental elements of the theory (Boolean equations and satisfiability problems, prime implicants and associated short representations, dualization), an in-depth study of special classes of Boolean functions (quadratic, Horn, shellable, regular, threshold, read-once functions and their characterization by functional equations) and two fruitful generalizations of the concept of Boolean functions (partially defined functions and pseudo-Boolean functions). Several topics are presented here in book form for the first time. Because of the depth and breadth and its emphasis on algorithms and applications, this monograph will have special appeal for researchers and graduate students in discrete mathematics, operations research, computer science, engineering and economics.

This two volume set LNCS 8634 and LNCS 8635 constitutes the refereed conference proceedings of the 39th International Symposium on Mathematical Foundations of Computer Science, MFCS 2014, held in Budapest, Hungary, in August 2014. The 95 revised full papers presented together with 6 invited talks were carefully selected from 270 submissions. The focus of the conference was on following topics: Logic, Semantics, Automata, Theory of Programming, Algorithms, Complexity, Parallel and Distributed Computing, Quantum Computing, Automata, Grammars and Formal Languages, Combinatorics on Words, Trees and Games.

A complete, accessible book on single and multiple output Boolean functions in cryptography and coding, with recent applications and problems.

This book constitutes the proceedings of the 14th International Computer Science Symposium in Russia, CSR 2019, held in Novosibirsk, Russia, in July 2019. The 31 full papers were carefully reviewed and selected from 71 submissions. The papers cover a wide range of topics such as algorithms and data structures; computational complexity; randomness in computing; approximation algorithms; combinatorial optimization; constraint satisfaction; computational geometry; formal languages and automata; codes and cryptography; combinatorics in computer science; applications of logic to computer science; proof complexity; fundamentals of machine learning; and theoretical aspects of big data.

This book presents interesting, important unsolved problems in the mathematical and computational sciences. The contributing authors are leading researchers in their fields and they explain outstanding challenges in their domains, first by offering basic definitions, explaining the context, and summarizing related algorithms, theorems, and proofs, and then by suggesting creative solutions. The authors feel a strong motivation to excite deep research and discussion in the mathematical and computational sciences community, and the book will be of value to postgraduate students and researchers in the areas of theoretical computer science, discrete mathematics, engineering, and cryptology.

Handbook of Discrete and Combinatorial Mathematics provides a comprehensive reference volume for mathematicians, computer scientists, engineers, as well as students and reference librarians. The material is presented so that key information can be located and used quickly and easily. Each chapter includes a glossary. Individual topics are covered in sections and subsections within chapters, each of which is organized into clearly identifiable parts: definitions, facts, and examples. Examples are provided to illustrate some of the key definitions, facts, and algorithms. Some curious and entertaining facts and puzzles are also included. Readers will also find an extensive collection of biographies. This second edition is a major revision. It includes extensive additions and updates. Since the first edition appeared in 1999, many new discoveries have been made and new areas have grown in importance, which are covered in this edition.

This book gives a detailed survey of the main results on bent functions over finite fields, presents a systematic overview of their generalizations, variations and applications, considers open problems in classification and systematization of bent functions, and discusses proofs of several results. This book uniquely provides a necessary comprehensive coverage of bent functions.It serves as a useful reference for researchers in discrete mathematics, coding and cryptography. Students and professors in mathematics and computer science will also find the content valuable, especially those interested in mathematical foundations of cryptography. It can be used as a supplementary text for university courses on discrete mathematics, Boolean functions, or cryptography, and is appropriate for both basic classes for under-graduate students and advanced courses for specialists in cryptography and mathematics.