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Part of: Synthesis digital library of engineering and computer science.

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Includes bibliographical references and index.

Preface -- 1. Equivalence classes of Boolean functions / Radomir S. Stanković, Stanislav Stanković, Helena Astola, and Jaakko T. Astola: Chapter summary; 1.1. Introduction; 1.2. Classification of switching functions; 1.3. NPN-classification; 1.4. LP-classification; 1.5. SD-classification; 1.6. Classification bywalsh coefficients; 1.7. Classification using decision diagrams; 1.8. Closing remarks; Acknowldegments; 1.9. Exercises; Bibliography -- 2. Boolean functions for cryptography / Jon T. Butler and Tsutomu Sasao: Chapter summary; 2.1. Introduction; 2.2. Properties of bent functions; 2.3. Properties of symmetric bent functions; 2.4. The strict avalanche criterion; 2.5. The propagation criterion; 2.6. Correlation immunity; 2.7. Concluding remarks; 2.8. Exercises; Bibliography -- 3. Boolean differential calculus / Bernd Steinbach and Christian Posthoff: Chapter summary; 3.1. Introduction; 3.2. Preliminaries; 3.3. Simple derivative operations; 3.4. Vectorial derivative operations; 3.5. m-fold derivative operations; 3.6. Applications to hazard detection; 3.7. Applications to decomposition; 3.8. Application to test pattern generation; 3.9. Generalization to differential operations; 3.10. Summary; 3.11. Exercises; Bibliography -- 4. Synthesis of Boolean functions in reversible logic / Robert Wille and Rolf Drechsler: Chapter summary; 4.1. Introduction; 4.2. Reversible logic; 4.3. Embedding irreversible functions; 4.4. Exact synthesis; 4.5. Heuristic synthesis; 4.6. BDD-based synthesis for large functions; 4.7. Conclusions and futurework; 4.8. Exercises; Bibliography -- 5. Data mining using binary decision diagrams / Shin-ichi Minato: Chapter summary; 5.1. Introduction; 5.2. BDD-based database representation; 5.3. LCM over ZDDs for large-scale itemset mining; 5.4. Application of LCM over ZDDs for finding distinctive itemsets; 5.5. Conclusion; 5.6. Exercises; Bibliography -- A. Solutions -- Index -- Authors' biographies.

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This book brings together five topics on the application of Boolean functions. They are: 1. Equivalence classes of Boolean functions: The number of n-variable functions is large, even for values as small as n = 6, and there has been much research on classifying functions. There are many classifications, each with its own distinct merit. 2. Boolean functions for cryptography: The process of encrypting/decrypting plaintext messages often depends on Boolean functions with specific properties. For example, highly nonlinear functions are valued because they are less susceptible to linear attacks. 3. Boolean differential calculus: An operation analogous to taking the derivative of a real-valued function offers important insight into the properties of Boolean functions. One can determine tests or susceptibility to hazards. 4. Reversible logic: Most logic functions are irreversible; it is impossible to reconstruct the input, given the output. However, Boolean functions that are reversible are necessary for quantum computing, and hold significant promise for low-power computing. 5. Data mining: The process of extracting subtle patterns from enormous amounts of data has benefited from the use of a graph-based representation of Boolean functions. This has use in surveillance, fraud detection, scientific discovery including bio-informatics, genetics, medicine, and education. Written by experts, these chapters present a tutorial view of new and emerging technologies in Boolean functions.

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