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Lattice functions and equations. (English) Zbl 0984.06001
Discrete Mathematics and Theoretical Computer Science. London: Springer. xi, 435 p. (2001).
This is a companion of the author’s earlier monograph: Boolean functions and equations, North-Holland, Amsterdam (1974; Zbl 0321.06013), subsequently quoted as BFE. Several results and concepts presented in BFE are updated and new results are specified in a more general context furnished by the lattice structure. Several applications in graph theory, synthesis of circuits, fault detection, databases and marketing are presented. The book is self-contained, includes a list of open problems and can be used successfully by graduate students in advanced studies. Computer scientists and mathematicians will find useful material for their research.
Contents: Exotic equations; Universal algebra; Lattices; Equational compactness of lattices and Boolean algebras; Post algebras; A revision of Boolean fundamentals; Closure operators on Boolean functions; Boolean transformations; Boolean differential calculus; Decomposition of Boolean functions; Boolean-based mathematics; Applications.

MSC:
06-02 Research exposition (monographs, survey articles) pertaining to ordered structures
06E30 Boolean functions
06B99 Lattices
94C10 Switching theory, application of Boolean algebra; Boolean functions (MSC2010)
94C12 Fault detection; testing in circuits and networks
03G10 Logical aspects of lattices and related structures
03G05 Logical aspects of Boolean algebras
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