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Chapter 15: Complete Systems of Boolean Functions and Bases

  • Alexander I. Kheyfits
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Discrete Mathematics With Cryptographic Applications
This chapter is in the book Discrete Mathematics With Cryptographic Applications
© 2021 Walter de Gruyter GmbH, Berlin/Boston

© 2021 Walter de Gruyter GmbH, Berlin/Boston

Chapters in this book

  1. Frontmatter i
  2. Contents v
  3. Preface xi
  4. Chapter 1: A Brief Survey of Elementary Functions 1
  5. Chapter 2: Propositional Algebra 27
  6. Chapter 3: Naïve and Formal (Axiomatic) Set Theory 51
  7. Chapter 4: Groups, Rings, and Fields 67
  8. Chapter 5: Predicates and Quantifiers—Algebraic Theory 79
  9. Chapter 6: Binary Relations and Relational Databases 93
  10. Chapter 7: Combinatorics 117
  11. Chapter 8: Elements of Number Theory 139
  12. Chapter 9: Boolean Functions 163
  13. Chapter 10: Hashing Functions and Cryptographic Maps 171
  14. Chapter 11: Generating Polynomials and Inversion Formulas 179
  15. Chapter 12: Systems of Representatives 187
  16. Chapter 13: Boolean Algebras 193
  17. Chapter 14: Combinatorial Circuits 201
  18. Chapter 15: Complete Systems of Boolean Functions and Bases 211
  19. Chapter 16: Introductory Graph Theory, Euler’s Formula, and Unbreakable Ciphers 225
  20. Chapter 17: Trees and Digraphs 245
  21. Chapter 18: Computations and Algorithms 263
  22. Chapter 19: Finite Automata 271
  23. Chapter 20: Introduction to Game Theory 297
  24. Chapter 21: Information Theory and Coding 309
  25. Chapter 22: Probability Theory with a Finite Sample Space and the Birthday Problem 319
  26. Chapter 23: Turing Machines, P and NP Classes, and Other Models of Computation 341
  27. Chapter 24: Answers and Solutions to Selected Exercises 351
  28. Bibliography 361
  29. Index 365
https://doi.org/10.1515/9781683927624-016

Chapters in this book

  1. Frontmatter i
  2. Contents v
  3. Preface xi
  4. Chapter 1: A Brief Survey of Elementary Functions 1
  5. Chapter 2: Propositional Algebra 27
  6. Chapter 3: Naïve and Formal (Axiomatic) Set Theory 51
  7. Chapter 4: Groups, Rings, and Fields 67
  8. Chapter 5: Predicates and Quantifiers—Algebraic Theory 79
  9. Chapter 6: Binary Relations and Relational Databases 93
  10. Chapter 7: Combinatorics 117
  11. Chapter 8: Elements of Number Theory 139
  12. Chapter 9: Boolean Functions 163
  13. Chapter 10: Hashing Functions and Cryptographic Maps 171
  14. Chapter 11: Generating Polynomials and Inversion Formulas 179
  15. Chapter 12: Systems of Representatives 187
  16. Chapter 13: Boolean Algebras 193
  17. Chapter 14: Combinatorial Circuits 201
  18. Chapter 15: Complete Systems of Boolean Functions and Bases 211
  19. Chapter 16: Introductory Graph Theory, Euler’s Formula, and Unbreakable Ciphers 225
  20. Chapter 17: Trees and Digraphs 245
  21. Chapter 18: Computations and Algorithms 263
  22. Chapter 19: Finite Automata 271
  23. Chapter 20: Introduction to Game Theory 297
  24. Chapter 21: Information Theory and Coding 309
  25. Chapter 22: Probability Theory with a Finite Sample Space and the Birthday Problem 319
  26. Chapter 23: Turing Machines, P and NP Classes, and Other Models of Computation 341
  27. Chapter 24: Answers and Solutions to Selected Exercises 351
  28. Bibliography 361
  29. Index 365
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