Résumé
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.
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.
Contents
- 1 Exotic equations 1
- 2 Universal algebra 13
- 3 Lattices 31
- 4 Equational compactness of lattices and Boolean algebras 61
- 5 Post algebras 69
- 6 A revision of Boolean fundamentals 125
- 7 Closure operators on Boolean functions 177
- 8 Boolean transformations 209
- 9 More on solving Boolean equations 231
- 10 Boolean differential calculus 267
- 11 Decomposition of Boolean functions 289
- 12 Boolean-based mathematics 303
- 13 Miscellanea 329
- 14 Applications 359
- App. 1 Errata to BFE 395
- App. 2 Decomposition of Boolean functions and applications: a bibliography 397
- App. 3: Open problems 405
- Bibliography 407
- Index
Caractéristiques techniques
| PAPIER | |
| Éditeur(s) | Springer |
| Auteur(s) | Sergiu Rudeanu |
| Parution | 18/10/2001 |
| Nb. de pages | 436 |
| Format | 15,5 x 23,5 |
| Couverture | Broché |
| Poids | 680g |
| Intérieur | Noir et Blanc |
| EAN13 | 9781852332662 |
| ISBN13 | 978-1-85233-266-2 |
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