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'

Integer Prograw~ing is one of the most fascinating and difficult areas in the field of Mathematical Optimization. Due to this fact notable research contributions to Integer Programming have been made in very different branches of mathematics and its applications. Since these publications are scattered over many journals, proceedings volumes, monographs, and working papers, a comprehensive bibliography of all these sources is a helpful tool even for specialists in this field. I initiated this compilation of literature in 1970 at the Institut fur ~konometrie und Operations Research, University of Bonn. Since then many collaborators have contributed to and worked on it. Among them Dipl.-Math. Claus Kastning has done the bulk of the work. With great perseverance and diligence he has gathered all the material and checked it with the original sources. The main aim was to incorporate rare and not easily accessible sources like Russian journals, preprints or unpublished papers. Without the invaluable and dedicated engagement of Claus Kastning the bibliography would never have reached this final version. For this reason he must be considered its responsible editor. As with any other collection this literature list has a subjective viewpoint and may be in some sense incomplete. We have however tried to be as complete as possible. The bibliography contains 4704 different publications by 6767 authors which were classified by 11839 descriptor entries.

Written by prominent experts in the field, this monograph provides the first comprehensive, 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. This framework looks at the fundamental elements of the theory (Boolean equations and satisfiability problems, prime implicants and associated short representations, dualization), an in-depth 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 for the first time. Because of the depth and breadth 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.

This proceedings volume contains extended abstracts of talks presented at the 18th Symposium on Operations Research held at the University of Cologne, September 1-3, 1993. The Symposia on Operations Research are the annual meetings of the Gesellschaft fiir Mathematik, Okonometrie und Operations Research (GMOOR), a scientific society providing a link between research and applications in the areas of applied mathematics, economics and operations research. The broad range of interests and scientific activities covered by GMOOR and its members was demonstrated by about 250 talks presented at the 18th Symposium. As in l'ecent years, emphasis was placed on optimization and stochastics, this year with a special focus on combinatorial optimization and discrete mathematics. We appreciate that with sections on parallel and distributed computing and on scientific computing also new fields could be integrated into the scope of the GMOOR. This book contains extended abstracts of most of the papers presented at the con ference. Long versions and full papers of the talks are expected to appear elsewhere in refereed periodicals. The contributions were divided into sixteen sections: (1) Theory of Optimization, (2) Computational Methods of Optimization, (3) Combinatorial Optimization and Dis crete Mathematics, (4) Scientific Computing, (5) Decision Theory, (6) Mathematical Economics and Game Theory, (7) Banking, Finance and Insurance, (8) Econometrics, (9) Macroeconomics and Economic Theory, (10) Stochastics, (11) Production and Lo gistics, (12) System and Control Theory, (13) Routing and Scheduling, (14) Knowledge Based Systems, (15) Information Systems and (16) Parallel and Distributed Compu ting.

A collection of papers written by prominent experts that examine a variety of advanced topics related to Boolean functions and expressions.

A comprehensive work in finite-value systems that covers the latest achievements using the semi-tensor product method, on various kinds of finite-value systems. These results occupy the highest position in the analysis and control of this field. It not only covers all aspects of research in finite-value systems, but also presents the mathematical derivation for each conclusion in depth. The book contains examples to provide a better understanding of the practical applications of finite-value systems. It will serve as a textbook for graduate students of Cybernetics, Mathematical, and Biology, and a reference for readers interested in the theory of finite-value systems.