Includes bibliographical references and index. "Written by prominent experts in the field, this monograph provides the first comprehensive and unified presentation of the structural, algorithmic, and applied aspects of the theory of Boolean functions. The book focuses on algebraic representations of Boolean functions, especially disjunctive and conjunctive normal form representations. It presents with in this framework the fundamental elements of the theory (Boolean equations and satisfiability problems, prime implicants and associated short representations, dualization), an indepth study of special classes of Boolean functions (quadratic, Horn, shellable, regular, threshold, read-once functions and their characterization by functional equations), and two fruitful generalizations of the concept of Boolean functions (partially defined functions and pseudo-Boolean functions). Several topics are presented here in book form forthe first time. Because of the unique depth and breadth of the unified treatment that it provides and its emphasis on algorithms and applications, this monograph will have special appeal for researchers and graduate students in discrete mathematics, operations research, computer science, engineering, and economics"-- Provided by publisher.
Contents:
Fundamental concepts and applications -- Boolean equations -- Prime implicants and minimal DNFs / Peter L. Hammer and Alexander Kogan -- Duality theory / Yves Crama and Kazuhisa Makino -- Quadratic functions / Bruno Simeone -- Horn functions / Endre Boros -- Orthogonal forms and shellability -- Regular functions -- Threshold functions -- Red-once functions / Martin C. Golumbic and Vladimir Gurvich -- Characterizations of special classes by functional equations / Lisa Hellerstein -- Partially defined Boolean functions / Toshihide Ibaraki -- Pseudo-Boolean functions -- Graphs and hypergraphs -- Algorithmic complexity -- JBool : a software tool / Claude Benzaken and Nadia Brauner.
Series:
Encyclopedia of mathematics and its applications ; 142
This resource is supported by the Institute of Museum and Library Services under the provisions of the Library Services and Technology Act as administered by State Library of Iowa.