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.
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