Lattice Functions and Equations

  • Sergiu┬áRudeanu

Part of the Discrete Mathematics and Theoretical Computer Science book series (DISCMATH)

Table of contents

  1. Front Matter
    Pages i-xi
  2. Sergiu Rudeanu
    Pages 1-12
  3. Sergiu Rudeanu
    Pages 13-30
  4. Sergiu Rudeanu
    Pages 31-60
  5. Sergiu Rudeanu
    Pages 69-123
  6. Sergiu Rudeanu
    Pages 125-176
  7. Sergiu Rudeanu
    Pages 177-207
  8. Sergiu Rudeanu
    Pages 209-230
  9. Sergiu Rudeanu
    Pages 231-266
  10. Sergiu Rudeanu
    Pages 267-288
  11. Sergiu Rudeanu
    Pages 289-302
  12. Sergiu Rudeanu
    Pages 303-327
  13. Sergiu Rudeanu
    Pages 329-358
  14. Sergiu Rudeanu
    Pages 359-394
  15. Back Matter
    Pages 395-436

About this book

Introduction

Lattice (Boolean) functions are algebraic functions defined over an arbitrary lattice (Boolean algebra), while lattice (Boolean) equations are equations expressed in terms of lattice (Boolean) functions.
This self-contained monograph surveys recent developments of Boolean functions and equations, as well as lattice functions and equations in more general classes of lattices; a special attention is paid to consistency conditions and reproductive general solutions.
The contents include:
- equational compactness in semilattices and Boolean algebras;
- the theory of Post functions and equations (which is very close to that of Boolean functions and equations);
- a revision of Boolean fundamentals;
- closure operators on Boolean functions;
- the decomposition of Boolean functions;
- quadratic truth equations;
- Boolean differential calculus;
- Boolean geometry and other topics.
There is also a chapter on equations in a very general sense. Applications refer to graph theory, automata theory, synthesis of circuits, fault detection, databases, marketing and others.

Keywords

Algebra Boolean Algebras Boolean algebra Boolean function Lattice Equations Lattice Functions automata logic mathematical logic

Authors and affiliations

  • Sergiu┬áRudeanu
    • 1
  1. 1.Faculty of MathematicsUniversity of BucharestBucharestRomania

Bibliographic information

  • DOI https://doi.org/10.1007/978-1-4471-0241-0
  • Copyright Information Springer-Verlag London Limited 2001
  • Publisher Name Springer, London
  • eBook Packages Springer Book Archive
  • Print ISBN 978-1-85233-266-2
  • Online ISBN 978-1-4471-0241-0
  • About this book