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| analysis of boolean functions: Analysis of Boolean Functions Ryan O'Donnell, 2014-06-05 This graduate-level text gives a thorough overview of the analysis of Boolean functions, beginning with the most basic definitions and proceeding to advanced topics. |
| analysis of boolean functions: Analysis of Boolean Functions Ryan O'Donnell, 2014-06-05 Boolean functions are perhaps the most basic objects of study in theoretical computer science. They also arise in other areas of mathematics, including combinatorics, statistical physics, and mathematical social choice. The field of analysis of Boolean functions seeks to understand them via their Fourier transform and other analytic methods. This text gives a thorough overview of the field, beginning with the most basic definitions and proceeding to advanced topics such as hypercontractivity and isoperimetry. Each chapter includes a 'highlight application' such as Arrow's theorem from economics, the Goldreich–Levin algorithm from cryptography/learning theory, Håstad's NP-hardness of approximation results, and 'sharp threshold' theorems for random graph properties. The book includes roughly 450 exercises and can be used as the basis of a one-semester graduate course. It should appeal to advanced undergraduates, graduate students and researchers in computer science theory and related mathematical fields. |
| analysis of boolean functions: Analysis of Boolean Functions Ryan O'Donnell, 2014 Boolean functions are perhaps the most basic objects of study in theoretical computer science. They also arise in other areas of mathematics, including combinatorics, statistical physics, and mathematical social choice. The field of analysis of Boolean functions seeks to understand them via their Fourier transform and other analytic methods. This text gives a thorough overview of the field, beginning with the most basic definitions and proceeding to advanced topics such as hypercontractivity and isoperimetry. Each chapter includes a 'highlight application' such as Arrow's theorem from economics, the Goldreich-Levin algorithm from cryptography/learning theory, Håstad's NP-hardness of approximation results, and 'sharp threshold' theorems for random graph properties. The book includes roughly 450 exercises and can be used as the basis of a one-semester graduate course. It should appeal to advanced undergraduates, graduate students and researchers in computer science theory and related mathematical fields. |
| analysis of boolean functions: Analysis of Boolean Functions Ryan O'Donnell, 2014 Boolean functions are perhaps the most basic objects of study in theoretical computer science. They also arise in other areas of mathematics, including combinatorics, statistical physics, and mathematical social choice. The field of analysis of Boolean functions seeks to understand them via their Fourier transform and other analytic methods. This text gives a thorough overview of the field, beginning with the most basic definitions and proceeding to advanced topics such as hypercontractivity and isoperimetry. Each chapter includes a 'highlight application' such as Arrow's theorem from economics, the Goldreich-Levin algorithm from cryptography/learning theory, Håstad's NP-hardness of approximation results, and 'sharp threshold' theorems for random graph properties. The book includes roughly 450 exercises and can be used as the basis of a one-semester graduate course. It should appeal to advanced undergraduates, graduate students and researchers in computer science theory and related mathematical fields. |
| analysis of boolean functions: Cryptographic Boolean Functions and Applications Thomas W. Cusick, Pantelimon Stanica, 2009-03-04 Boolean functions are the building blocks of symmetric cryptographic systems. Symmetrical cryptographic algorithms are fundamental tools in the design of all types of digital security systems (i.e. communications, financial and e-commerce).Cryptographic Boolean Functions and Applications is a concise reference that shows how Boolean functions are used in cryptography. Currently, practitioners who need to apply Boolean functions in the design of cryptographic algorithms and protocols need to patch together needed information from a variety of resources (books, journal articles and other sources). This book compiles the key essential information in one easy to use, step-by-step reference. Beginning with the basics of the necessary theory the book goes on to examine more technical topics, some of which are at the frontier of current research. Serves as a complete resource for the successful design or implementation of cryptographic algorithms or protocols using Boolean functions Provides engineers and scientists with a needed reference for the use of Boolean functions in cryptography Addresses the issues of cryptographic Boolean functions theory and applications in one concentrated resource Organized logically to help the reader easily understand the topic |
| analysis of boolean functions: Noise Sensitivity of Boolean Functions and Percolation Christophe Garban, Jeffrey E. Steif, 2015 This is the first book to cover the theory of noise sensitivity of Boolean functions with particular emphasis on critical percolation. |
| analysis of boolean functions: Boolean Valued Analysis A.G. Kusraev, Semën Samsonovich Kutateladze, 2012-12-06 Boolean valued analysis is a technique for studying properties of an arbitrary mathematical object by comparing its representations in two different set-theoretic models whose construction utilises principally distinct Boolean algebras. The use of two models for studying a single object is a characteristic of the so-called non-standard methods of analysis. Application of Boolean valued models to problems of analysis rests ultimately on the procedures of ascending and descending, the two natural functors acting between a new Boolean valued universe and the von Neumann universe. This book demonstrates the main advantages of Boolean valued analysis which provides the tools for transforming, for example, function spaces to subsets of the reals, operators to functionals, and vector-functions to numerical mappings. Boolean valued representations of algebraic systems, Banach spaces, and involutive algebras are examined thoroughly. Audience: This volume is intended for classical analysts seeking powerful new tools, and for model theorists in search of challenging applications of nonstandard models. |
| analysis of boolean functions: Boolean Functions Yves Crama, Peter L. Hammer, 2011-05-16 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. |
| analysis of boolean functions: Boolean Function Complexity Stasys Jukna, 2012-01-06 Boolean circuit complexity is the combinatorics of computer science and involves many intriguing problems that are easy to state and explain, even for the layman. This book is a comprehensive description of basic lower bound arguments, covering many of the gems of this “complexity Waterloo” that have been discovered over the past several decades, right up to results from the last year or two. Many open problems, marked as Research Problems, are mentioned along the way. The problems are mainly of combinatorial flavor but their solutions could have great consequences in circuit complexity and computer science. The book will be of interest to graduate students and researchers in the fields of computer science and discrete mathematics. |
| analysis of boolean functions: Boolean Functions for Cryptography and Coding Theory Claude Carlet, 2021-01-07 Boolean functions are essential to systems for secure and reliable communication. This comprehensive survey of Boolean functions for cryptography and coding covers the whole domain and all important results, building on the author's influential articles with additional topics and recent results. A useful resource for researchers and graduate students, the book balances detailed discussions of properties and parameters with examples of various types of cryptographic attacks that motivate the consideration of these parameters. It provides all the necessary background on mathematics, cryptography, and coding, and an overview on recent applications, such as side channel attacks on smart cards, cloud computing through fully homomorphic encryption, and local pseudo-random generators. The result is a complete and accessible text on the state of the art in single and multiple output Boolean functions that illustrates the interaction between mathematics, computer science, and telecommunications. |
| analysis of boolean functions: Analysis and Control of Boolean Networks Daizhan Cheng, Hongsheng Qi, Zhiqiang Li, 2010-11-23 Analysis and Control of Boolean Networks presents a systematic new approach to the investigation of Boolean control networks. The fundamental tool in this approach is a novel matrix product called the semi-tensor product (STP). Using the STP, a logical function can be expressed as a conventional discrete-time linear system. In the light of this linear expression, certain major issues concerning Boolean network topology – fixed points, cycles, transient times and basins of attractors – can be easily revealed by a set of formulae. This framework renders the state-space approach to dynamic control systems applicable to Boolean control networks. The bilinear-systemic representation of a Boolean control network makes it possible to investigate basic control problems including controllability, observability, stabilization, disturbance decoupling etc. |
| analysis of boolean functions: Quantum Algorithms for Cryptographically Significant Boolean Functions Tharrmashastha SAPV, Debajyoti Bera, Arpita Maitra, Subhamoy Maitra, 2021-07-19 This book is a timely report of the state-of-the-art analytical techniques in the domain of quantum algorithms related to Boolean functions. It bridges the gap between recent developments in the area and the hands-on analysis of the spectral properties of Boolean functions from a cryptologic viewpoint. Topics covered in the book include Qubit, Deutsch–Jozsa and Walsh spectrum, Grover’s algorithm, Simon’s algorithm and autocorrelation spectrum. The book aims at encouraging readers to design and implement practical algorithms related to Boolean functions. Apart from combinatorial techniques, this book considers implementing related programs in a quantum computer. Researchers, practitioners and educators will find this book valuable. |
| analysis of boolean functions: Boolean Models and Methods in Mathematics, Computer Science, and Engineering Yves Crama, Peter L. Hammer, 2010-06-28 A collection of papers written by prominent experts that examine a variety of advanced topics related to Boolean functions and expressions. |
| analysis of boolean functions: The Complexity of Boolean Functions Ingo Wegener, 1987 |
| analysis of boolean functions: Boolean Reasoning Frank Markham Brown, 2012-02-10 Concise text begins with overview of elementary mathematical concepts and outlines theory of Boolean algebras; defines operators for elimination, division, and expansion; covers syllogistic reasoning, solution of Boolean equations, functional deduction. 1990 edition. |
| analysis of boolean functions: Bent Functions Natalia Tokareva, 2015-08-24 Bent Functions: Results and Applications to Cryptography offers a unique survey of the objects of discrete mathematics known as Boolean bent functions. As these maximal, nonlinear Boolean functions and their generalizations have many theoretical and practical applications in combinatorics, coding theory, and cryptography, the text provides a detailed survey of their main results, presenting a systematic overview of their generalizations and applications, and considering open problems in classification and systematization of bent functions. The text is appropriate for novices and advanced researchers, discussing proofs of several results, including the automorphism group of bent functions, the lower bound for the number of bent functions, and more. - Provides a detailed survey of bent functions and their main results, presenting a systematic overview of their generalizations and applications - Presents a systematic and detailed survey of hundreds of results in the area of highly nonlinear Boolean functions in cryptography - Appropriate coverage for students from advanced specialists in cryptography, mathematics, and creators of ciphers |
| analysis of boolean functions: Logic and Boolean Algebra Bradford Henry Arnold, 2011-01-01 Orignally published: Englewood Cliffs, N.J.: Prentice-Hall, 1962. |
| analysis of boolean functions: Complexity Classifications of Boolean Constraint Satisfaction Problems Nadia Creignou, Sanjeev Khanna, Madhu Sudan, 2001-01-01 Presents a novel form of a compendium that classifies an infinite number of problems by using a rule-based approach. |
| analysis of boolean functions: Boolean Functions Winfried G. Schneeweiss, 2012-12-06 Modern systems engineering (e. g. switching circuits design) and operations research (e. g. reliability systems theory) use Boolean functions with increasing regularity. For practitioners and students in these fields books written for mathe maticians are in several respects not the best source of easy to use information, and standard books, such as, on switching circuits theory and reliability theory, are mostly somewhat narrow as far as Boolean analysis is concerned. Further more, in books on switching circuits theory the relevant stochastic theory is not covered. Aspects of the probabilistic theory of Boolean functions are treated in some works on reliability theory, but the results deserve a much broader interpre tation. Just as the applied theory (e. g. of the Laplace transform) is useful in control theory, renewal theory, queueing theory, etc. , the applied theory of Boolean functions (of indicator variables) can be useful in reliability theory, switching circuits theory, digital diagnostics and communications theory. This book is aimed at providing a sufficiently deep understanding of useful results both in practical work and in applied research. Boolean variables are restricted here to indicator or O/l variables, i. e. variables whose values, namely 0 and 1, are not free for a wide range of interpretations, e. g. in digital electronics 0 for L ==low voltage and 1 for H == high voltage. |
| analysis of boolean functions: Higher Order Fourier Analysis Terence Tao, 2012-12-30 Higher order Fourier analysis is a subject that has become very active only recently. This book serves as an introduction to the field, giving the beginning graduate student in the subject a high-level overview of the field. The text focuses on the simplest illustrative examples of key results, serving as a companion to the existing literature. |
| analysis of boolean functions: Introduction to Property Testing Oded Goldreich, 2017-11-23 An extensive and authoritative introduction to property testing, the study of super-fast algorithms for the structural analysis of large quantities of data in order to determine global properties. This book can be used both as a reference book and a textbook, and includes numerous exercises. |
| analysis of boolean functions: Boolean Differential Equations Bernd Steinbach, Christian Posthoff, 2013-06-01 The Boolean Differential Calculus (BDC) is a very powerful theory that extends the structure of a Boolean Algebra significantly. Based on a small number of definitions, many theorems have been proven. The available operations have been efficiently implemented in several software packages. There is a very wide field of applications. While a Boolean Algebra is focused on values of logic functions, the BDC allows the evaluation of changes of function values. Such changes can be explored for pairs of function values as well as for whole subspaces. Due to the same basic data structures, the BDC can be applied to any task described by logic functions and equations together with the Boolean Algebra. The BDC can be widely used for the analysis, synthesis, and testing of digital circuits. Generally speaking, a Boolean differential equation (BDE) is an equation in which elements of the BDC appear. It includes variables, functions, and derivative operations of these functions. The solution of such a BDE is a set of Boolean functions. This is a significant extension of Boolean equations, which have sets of Boolean vectors as solutions. In the simplest BDE a derivative operation of the BDC on the left-hand side is equal to a logic function on the right-hand side. The solution of such a simple BDE means to execute an operation which is inverse to the given derivative. BDEs can be applied in the same fields as the BDC, however, their possibility to express sets of Boolean functions extends the application field significantly. |
| analysis of boolean functions: Analytic Combinatorics Philippe Flajolet, Robert Sedgewick, 2009-01-15 Analytic combinatorics aims to enable precise quantitative predictions of the properties of large combinatorial structures. The theory has emerged over recent decades as essential both for the analysis of algorithms and for the study of scientific models in many disciplines, including probability theory, statistical physics, computational biology, and information theory. With a careful combination of symbolic enumeration methods and complex analysis, drawing heavily on generating functions, results of sweeping generality emerge that can be applied in particular to fundamental structures such as permutations, sequences, strings, walks, paths, trees, graphs and maps. This account is the definitive treatment of the topic. The authors give full coverage of the underlying mathematics and a thorough treatment of both classical and modern applications of the theory. The text is complemented with exercises, examples, appendices and notes to aid understanding. The book can be used for an advanced undergraduate or a graduate course, or for self-study. |
| analysis of boolean functions: Fourier Analysis on Finite Groups and Applications Audrey Terras, 1999-03-28 It examines the theory of finite groups in a manner that is both accessible to the beginner and suitable for graduate research. |
| analysis of boolean functions: Branching Programs and Binary Decision Diagrams Ingo Wegener, 2000-01-01 Finite functions (in particular, Boolean functions) play a fundamental role in computer science and discrete mathematics. This book describes representations of Boolean functions that have small size for many important functions and which allow efficient work with the represented functions. The representation size of important and selected functions is estimated, upper and lower bound techniques are studied, efficient algorithms for operations on these representations are presented, and the limits of those techniques are considered. This book is the first comprehensive description of theory and applications. Research areas like complexity theory, efficient algorithms, data structures, and discrete mathematics will benefit from the theory described in this book. The results described within have applications in verification, computer-aided design, model checking, and discrete mathematics. This is the only book to investigate the representation size of Boolean functions and efficient algorithms on these representations. |
| analysis of boolean functions: Probabilistic Boolean Networks Ilya Shmulevich, Edward R. Dougherty, 2010-01-21 The first comprehensive treatment of probabilistic Boolean networks, unifying different strands of current research and addressing emerging issues. |
| analysis of boolean functions: Advances in Cryptology--EUROCRYPT '90 Ivan Bjerre Damgård, 1991 Eurocrypt is a conference devoted to all aspects of cryptologic research, both theoretical and practical, sponsored by the International Association for Cryptologic Research (IACR). Eurocrypt 90 took place in Åarhus, Denmark, in May 1990. From the 85 papers submitted, 42 were selected for presentation at the conference and for inclusion in this volume. In addition to the formal contributions, short abstracts of a number of informal talks are included in these proceedings. The proceedings are organized into sessions on protocols, number-theoretic algorithms, boolean functions, binary sequences, implementations, combinatorial schemes, cryptanalysis, new cryptosystems, signatures and authentication, and impromptu talks. |
| analysis of boolean functions: Python Data Science Handbook Jake VanderPlas, 2016-11-21 For many researchers, Python is a first-class tool mainly because of its libraries for storing, manipulating, and gaining insight from data. Several resources exist for individual pieces of this data science stack, but only with the Python Data Science Handbook do you get them all—IPython, NumPy, Pandas, Matplotlib, Scikit-Learn, and other related tools. Working scientists and data crunchers familiar with reading and writing Python code will find this comprehensive desk reference ideal for tackling day-to-day issues: manipulating, transforming, and cleaning data; visualizing different types of data; and using data to build statistical or machine learning models. Quite simply, this is the must-have reference for scientific computing in Python. With this handbook, you’ll learn how to use: IPython and Jupyter: provide computational environments for data scientists using Python NumPy: includes the ndarray for efficient storage and manipulation of dense data arrays in Python Pandas: features the DataFrame for efficient storage and manipulation of labeled/columnar data in Python Matplotlib: includes capabilities for a flexible range of data visualizations in Python Scikit-Learn: for efficient and clean Python implementations of the most important and established machine learning algorithms |
| analysis of boolean functions: Spaces: An Introduction to Real Analysis Tom L. Lindstrøm, 2017-11-28 Spaces is a modern introduction to real analysis at the advanced undergraduate level. It is forward-looking in the sense that it first and foremost aims to provide students with the concepts and techniques they need in order to follow more advanced courses in mathematical analysis and neighboring fields. The only prerequisites are a solid understanding of calculus and linear algebra. Two introductory chapters will help students with the transition from computation-based calculus to theory-based analysis. The main topics covered are metric spaces, spaces of continuous functions, normed spaces, differentiation in normed spaces, measure and integration theory, and Fourier series. Although some of the topics are more advanced than what is usually found in books of this level, care is taken to present the material in a way that is suitable for the intended audience: concepts are carefully introduced and motivated, and proofs are presented in full detail. Applications to differential equations and Fourier analysis are used to illustrate the power of the theory, and exercises of all levels from routine to real challenges help students develop their skills and understanding. The text has been tested in classes at the University of Oslo over a number of years. |
| analysis of boolean functions: A Short Course in Discrete Mathematics Edward A. Bender, S. Gill Williamson, 2005-01-01 What sort of mathematics do I need for computer science? In response to this frequently asked question, a pair of professors at the University of California at San Diego created this text. Its sources are two of the university's most basic courses: Discrete Mathematics, and Mathematics for Algorithm and System Analysis. Intended for use by sophomores in the first of a two-quarter sequence, the text assumes some familiarity with calculus. Topics include Boolean functions and computer arithmetic; logic; number theory and cryptography; sets and functions; equivalence and order; and induction, sequences, and series. Multiple choice questions for review appear throughout the text. Original 2005 edition. Notation Index. Subject Index. |
| analysis of boolean functions: An Introduction to Measure Theory Terence Tao, 2021-09-03 This is a graduate text introducing the fundamentals of measure theory and integration theory, which is the foundation of modern real analysis. The text focuses first on the concrete setting of Lebesgue measure and the Lebesgue integral (which in turn is motivated by the more classical concepts of Jordan measure and the Riemann integral), before moving on to abstract measure and integration theory, including the standard convergence theorems, Fubini's theorem, and the Carathéodory extension theorem. Classical differentiation theorems, such as the Lebesgue and Rademacher differentiation theorems, are also covered, as are connections with probability theory. The material is intended to cover a quarter or semester's worth of material for a first graduate course in real analysis. There is an emphasis in the text on tying together the abstract and the concrete sides of the subject, using the latter to illustrate and motivate the former. The central role of key principles (such as Littlewood's three principles) as providing guiding intuition to the subject is also emphasized. There are a large number of exercises throughout that develop key aspects of the theory, and are thus an integral component of the text. As a supplementary section, a discussion of general problem-solving strategies in analysis is also given. The last three sections discuss optional topics related to the main matter of the book. |
| analysis of boolean functions: Computational Complexity Sanjeev Arora, Boaz Barak, 2009-04-20 New and classical results in computational complexity, including interactive proofs, PCP, derandomization, and quantum computation. Ideal for graduate students. |
| analysis of boolean functions: Analysis and Design of Stream Ciphers Rainer A. Rueppel, 2012-12-06 It is now a decade since the appearance of W. Diffie and M. E. Hellmann's startling paper, New Directions in Cryptography. This paper not only established the new field of public-key cryptography but also awakened scientific interest in secret-key cryptography, a field that had been the almost exclusive domain of secret agencies and mathematical hobbyist. A number of ex cellent books on the science of cryptography have appeared since 1976. In the main, these books thoroughly treat both public-key systems and block ciphers (i. e. secret-key ciphers with no memo ry in the enciphering transformation) but give short shrift to stream ciphers (i. e. , secret-key ciphers wi th memory in the enciphering transformation). Yet, stream ciphers, such as those . implemented by rotor machines, have played a dominant role in past cryptographic practice, and, as far as I can determine, re main still the workhorses of commercial, military and diplomatic secrecy systems. My own research interest in stream ciphers found a natural re sonance in one of my doctoral students at the Swiss Federal Institute of Technology in Zurich, Rainer A. Rueppe1. As Rainer was completing his dissertation in late 1984, the question arose as to where he should publish the many new results on stream ciphers that had sprung from his research. |
| analysis of boolean functions: Fourier Analysis Elias M. Stein, Rami Shakarchi, 2011-02-11 This first volume, a three-part introduction to the subject, is intended for students with a beginning knowledge of mathematical analysis who are motivated to discover the ideas that shape Fourier analysis. It begins with the simple conviction that Fourier arrived at in the early nineteenth century when studying problems in the physical sciences--that an arbitrary function can be written as an infinite sum of the most basic trigonometric functions. The first part implements this idea in terms of notions of convergence and summability of Fourier series, while highlighting applications such as the isoperimetric inequality and equidistribution. The second part deals with the Fourier transform and its applications to classical partial differential equations and the Radon transform; a clear introduction to the subject serves to avoid technical difficulties. The book closes with Fourier theory for finite abelian groups, which is applied to prime numbers in arithmetic progression. In organizing their exposition, the authors have carefully balanced an emphasis on key conceptual insights against the need to provide the technical underpinnings of rigorous analysis. Students of mathematics, physics, engineering and other sciences will find the theory and applications covered in this volume to be of real interest. The Princeton Lectures in Analysis represents a sustained effort to introduce the core areas of mathematical analysis while also illustrating the organic unity between them. Numerous examples and applications throughout its four planned volumes, of which Fourier Analysis is the first, highlight the far-reaching consequences of certain ideas in analysis to other fields of mathematics and a variety of sciences. Stein and Shakarchi move from an introduction addressing Fourier series and integrals to in-depth considerations of complex analysis; measure and integration theory, and Hilbert spaces; and, finally, further topics such as functional analysis, distributions and elements of probability theory. |
| analysis of boolean functions: Boolean Function Complexity Michael S. Paterson, 1992-11-05 Here Professor Paterson brings together papers from the 1990 Durham symposium on Boolean function complexity. The participants include many well known figures in the field. |
| analysis of boolean functions: Higher-Order Fourier Analysis and Applications Hamed Hatami, Pooya Hatami, Shachar Lovett, 2019-09-26 Higher-order Fourier Analysis and Applications provides an introduction to the field of higher-order Fourier analysis with an emphasis on its applications to theoretical computer science. Higher-order Fourier analysis is an extension of the classical Fourier analysis. It has been developed by several mathematicians over the past few decades in order to study problems in an area of mathematics called additive combinatorics, which is primarily concerned with linear patterns such as arithmetic progressions in subsets of integers. The monograph is divided into three parts: Part I discusses linearity testing and its generalization to higher degree polynomials. Part II present the fundamental results of the theory of higher-order Fourier analysis. Part III uses the tools developed in Part II to prove some general results about property testing for algebraic properties. It describes applications of the theory of higher-order Fourier analysis in theoretical computer science, and, to this end, presents the foundations of this theory through such applications; in particular to the area of property testing. |
| analysis of boolean functions: Advances in Cryptology -- EUROCRYPT 2003 Eli Biham, 2003-04-22 This book constitutes the refereed proceedings of the International Conference on the Theory and Applications of Cryptographic Techniques, EUROCRYPT 2003, held in Warsaw, Poland in May 2003. The 37 revised full papers presented together with two invited papers were carefully reviewed and selected from 156 submissions. The papers are organized in topical sections on cryptanalysis, secure multi-party communication, zero-knowledge protocols, foundations and complexity-theoretic security, public key encryption, new primitives, elliptic curve cryptography, digital signatures, information-theoretic cryptography, and group signatures. |
| analysis of boolean functions: Boolean Differential Calculus Bernd Steinbach, Christian Posthoff, 2022-05-31 The Boolean Differential Calculus (BDC) is a very powerful theory that extends the basic concepts of Boolean Algebras significantly. Its applications are based on Boolean spaces and n, Boolean operations, and basic structures such as Boolean Algebras and Boolean Rings, Boolean functions, Boolean equations, Boolean inequalities, incompletely specified Boolean functions, and Boolean lattices of Boolean functions. These basics, sometimes also called switching theory, are widely used in many modern information processing applications. The BDC extends the known concepts and allows the consideration of changes of function values. Such changes can be explored for pairs of function values as well as for whole subspaces. The BDC defines a small number of derivative and differential operations. Many existing theorems are very welcome and allow new insights due to possible transformations of problems. The available operations of the BDC have been efficiently implemented in several software packages. The common use of the basic concepts and the BDC opens a very wide field of applications. The roots of the BDC go back to the practical problem of testing digital circuits. The BDC deals with changes of signals which are very important in applications of the analysis and the synthesis of digital circuits. The comprehensive evaluation and utilization of properties of Boolean functions allow, for instance, to decompose Boolean functions very efficiently; this can be applied not only in circuit design, but also in data mining. Other examples for the use of the BDC are the detection of hazards or cryptography. The knowledge of the BDC gives the scientists and engineers an extended insight into Boolean problems leading to new applications, e.g., the use of Boolean lattices of Boolean functions. |
| analysis of boolean functions: Discrete Mathematics of Neural Networks Martin Anthony, 2001-01-01 This concise, readable book provides a sampling of the very large, active, and expanding field of artificial neural network theory. It considers select areas of discrete mathematics linking combinatorics and the theory of the simplest types of artificial neural networks. Neural networks have emerged as a key technology in many fields of application, and an understanding of the theories concerning what such systems can and cannot do is essential. Some classical results are presented with accessible proofs, together with some more recent perspectives, such as those obtained by considering decision lists. In addition, probabilistic models of neural network learning are discussed. Graph theory, some partially ordered set theory, computational complexity, and discrete probability are among the mathematical topics involved. Pointers to further reading and an extensive bibliography make this book a good starting point for research in discrete mathematics and neural networks. |
| analysis of boolean functions: Boolean Functions and Computation Models Peter Clote, Evangelos Kranakis, 2013-03-09 The two internationally renowned authors elucidate the structure of fast parallel computation. Its complexity is emphasised through a variety of techniques ranging from finite combinatorics, probability theory and finite group theory to finite model theory and proof theory. Non-uniform computation models are studied in the form of Boolean circuits; uniform ones in a variety of forms. Steps in the investigation of non-deterministic polynomial time are surveyed as is the complexity of various proof systems. Providing a survey of research in the field, the book will benefit advanced undergraduates and graduate students as well as researchers. |
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