Rudeanu S. Lattice functions and equations (London; New York, 2001). - ОГЛАВЛЕНИЕ / CONTENTS
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ОбложкаRudeanu S. Lattice functions and equations. - London; New York: Springer, 2001. - xi, 435 p. - (Discrete mathematics and theoretical computer science). - Bibliogr.: p.407-427. - Ind.: p.429-435. - ISBN 1-85233-266-2; ISSN 1439-9911
 

Оглавление / Contents
 
1  Exotic equations ............................................. 1
   1  An abstract theory of equations ........................... 1
   2  Equations over finite sets ................................ 5
2  Universal algebra ........................................... 13
   1  First concepts and subdirect decompositions .............. 13
   2  Term algebra, identities and polynomials ................. 17
   3  Polynomials, identities (continued) and algebraic
      functions ................................................ 22
3  Lattices .................................................... 31
   1  Posets and distributive lattices ......................... 31
   2  Classes of (relatively) (pseudo)complemented lattices .... 35
   3  Functions and equations .................................. 47
4  Equational compactness of lattices and Boolean algebras ..... 61
   1  Abstract equational compactness .......................... 61
   2  Equational monocompactness of semilattices and
      lattices ................................................. 62
   3  Equational compactness of Boolean algebras ............... 66
5  Post algebras ............................................... 69
   1  Basic properties of Post algebras ........................ 69
   2  Post functions ........................................... 83
   3  Post equations ........................................... 90
6  A revision of Boolean fundamentals ......................... 125
   1  Linear Boolean equations ................................ 125
   2  Generalized minterms and interpolating systems .......... 134
   3  Prime implicants and syllogistic forms .................. 141
   4  Reproductive solutions, recurrent inequalities and
      recurrent covers ........................................ l53
   5  Generalized systems/solutions of Boolean equations ...... 167
7  Closure operators on Boolean functions ..................... 177
   1  A general theory ........................................ 177
   2  Isotone and monotone closures ........................... 181
   3  Independent and decomposition closures .................. 192
8  Boolean transformations .................................... 209
   1  Functional dependence of Boolean functions .............. 209
   2  The range of a Boolean transformation ................... 216
   3  Injectivity domains of Boolean transformations .......... 219
   4  Fixed points of lattice and Boolean transformations ..... 225
9  More on solving Boolean equations .......................... 231
   1  Special methods for solving Boolean equations ........... 231
   2  Boolean equations with unique solution .................. 249
   3  Quadratic truth equations ............................... 253
   4  Boolean equations on computers .......................... 264
10 Boolean differential calculus .............................. 267
   1  An informal discussion .................................. 267
   2  An axiomatic approach ................................... 274
   3  Boolean differential equations .......................... 282
11 Decomposition of Boolean functions ......................... 289
   1  A historical sketch ..................................... 289
   2  Decomposition via Boolean equations ..................... 294
12 Boolean-based mathematics .................................. 303
   1  Mathematical logic ...................................... 303
   2  Post-based algebra ...................................... 312
   3  Geometry ................................................ 314
   4  Statistics .............................................. 324
13 Miscellanea ................................................ 329
   1  Equations in MVL and relation algebras .................. 329
   2  Equations in functionally complete algebras ............. 333
   3  Generalized Boolean functions and non-Boolean
      functions ............................................... 337
   4  Functional characterizations of classes of functions
      over В .................................................. 344
   5  Local properties of Boolean functions and extremal
      solutions of Boolean equations .......................... 349
14 Applications ............................................... 359
   1  Graph theory ............................................ 359
   2  Automata theory ......................................... 365
   3  Synthesis of circuits ................................... 372
   4  Fault detection in combinational circuits ............... 380
   5  Databases ............................................... 383
   6  Marketing ............................................... 386
   7  Other applications ...................................... 389

Appendix 1  Errata to BFE ..................................... 395
Appendix 2  Decomposition of Boolean functions and
            applications: a bibliography ...................... 397
Appendix 3  Open problems ..................................... 405
Bibliography .................................................. 429


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