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.

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.

Reviewer: N.Ţăndăreanu (Craiova)

##### 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 |