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140122 ||| eng |
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|a 9781447102410
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| 100 |
1 |
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|a Rudeanu, Sergiu
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| 245 |
0 |
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|a Lattice Functions and Equations
|h Elektronische Ressource
|c by Sergiu Rudeanu
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| 250 |
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|a 1st ed. 2001
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| 260 |
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|a London
|b Springer London
|c 2001, 2001
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| 300 |
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|a XI, 435 p. 1 illus
|b online resource
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| 505 |
0 |
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|a 1 Equations in MVL and relation algebras -- 2 Equations in functionally complete algebras -- 3 Generalized Boolean functions and non-Boolean functions -- 4 Functional characterizations of classes of functions over B -- 5 Local properties of Boolean functions and extremal solutions of Boolean equations -- 14. Applications -- 1 Graph theory -- 2 Automata theory -- 3 Synthesis of circuits -- 4 Fault detection in combinational circuits -- 5 Databases -- 6 Marketing -- 7 Other applications -- Appendix 1. Errata to BFE -- Appendix 2. Decomposition of Boolean functions and applications: a bibliography -- Appendix 3. Open problems
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| 505 |
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|a 5 Generalized systems/solutions of Boolean equations -- 7. Closure operators on Boolean functions -- 1 A general theory -- 2 Isotone and monotone closures -- 3 Independent and decomposition closures -- 8. Boolean transformations -- 1 Functional dependence of Boolean functions -- 2 The range of a Boolean transformation -- 3 Injectivity domains of Boolean transformations -- 4 Fixed points of lattice and Boolean transformations -- 9. More on solving Boolean equations -- 1 Special methods for solving Boolean equations -- 2 Boolean equations with unique solution -- 3 Quadratic truth equations -- 4 Boolean equations on computers -- 10. Boolean differential calculus -- 1 An informal discussion -- 2 An axiomatic approach -- 3 Boolean differential equations -- 11. Decomposition of Boolean functions -- 1 A historical sketch -- 2 Decomposition via Boolean equations -- 12. Boolean-based mathematics -- 1 Mathematical logic -- 2 Post-based algebra -- 3 Geometry -- 4 Statistics -- 13. Miscellanea --
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| 505 |
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|a 1. Exotic equations -- 1 An abstract theory of equations -- 2 Equations over finite sets -- 2. Universal algebra -- 1 First concepts and subdirect decompositions -- 2 Term algebra , ident ities and polynomials -- 3 Polynomials, identities (continued) and algebraic functions -- 3. Lattices -- 1 Posets and distributive lattices -- 2 Classes of (relatively) (pseudo)complemented lattices -- 3 Functions and equations -- 4. Equational compactness of lattices and Boolean algebras -- 1 Abstract equational compactness -- 2 Equational monocompactness of semilattices and lattices -- 3 Equational compactness of Boolean algebras -- 5. Post algebras -- 1 Basic properties of Post algebras -- 2 Post functions -- 3 Post equations -- 6. A revision of Boolean fundamentals -- 1 Linear Boolean equations -- 2 Generalized minterms and interpolating systems -- 3 Prime implicants and syllogistic forms -- 4 Reproductive solutions , recurrent inequalities and recurrent covers --
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| 653 |
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|a Mathematical Logic and Formal Languages
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| 653 |
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|a Mathematical logic
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| 653 |
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|a Algorithms
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| 653 |
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|a Algorithms
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| 653 |
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|a Algebra
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| 653 |
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|a Algorithm Analysis and Problem Complexity
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| 653 |
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|a Algebra
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| 041 |
0 |
7 |
|a eng
|2 ISO 639-2
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| 989 |
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|b SBA
|a Springer Book Archives -2004
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| 490 |
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|a Discrete Mathematics and Theoretical Computer Science
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| 856 |
4 |
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|u https://doi.org/10.1007/978-1-4471-0241-0?nosfx=y
|x Verlag
|3 Volltext
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| 082 |
0 |
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|a 512
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| 520 |
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|a 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
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