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In classical analysis, there is a vast difference between the class of problems that may be handled by means of the methods of calculus and the class of problems requiring combinatorial techniques. With the advent of the digital computer, the distinction begins to blur, and with the increasing emphasis on problems involving optimization over structures, tIlE' distinction vanishes. What is necessary for the analytic and computational treatment of significant questions arising in modern control theory, mathematical economics, scheduling theory, operations research, bioengineering, and so forth is a new and more flexible mathematical theory which subsumes both the cla8sical continuous and discrete t 19orithms. The work by HAMMER (IVANESCU) and RUDEANU on Boolean methods represents an important step in this dnectlOn, and it is thus a great pleasure to welcome it into print. It will certainly stimulate a great deal of additional research in both theory and application. RICHARD BELLMAN University of Southern California FOf(,WOl'
List of contents
I.- I. Boolean Algebra.- II. Boolean Equations.- III. Linear Pseudo-Boolean Equations and Inequalities.- IV. Nonlinear Pseudo-Boolean Equations and Inequalities.- V. Minimization of Linear Pseudo-Boolean Functions.- VI. Minimization of Nonlinear Pseudo-Boolean Functions.- VII. Extensions of Pseudo-Boolean Programming.- II.- VIII. Integer Mathematical Programming.- IX. Connectedness and Path Problems in Graphs.- X. Stable Sets, Kernels, and Chromatic Decompositions of Graphs.- XI. Matchings of Bipartite Graphs.- XII. Flows in Networks and Chains in Partially Ordered Sets.- XIII. Various Applications.- XIV. Minimization Problems in Automata Theory.- Appendix: Generalized Pseudo-Boolean Programming, by Ivo Rosenberg.- Conclusions.- Supplementary Bibliographies.- A. Boolean Equations and Generalizations.- B. Books on Boolean Algebra and Switching Theory.- Author Index.
