Applications of Continuous Mathematics to Computer Science
This volume is intended to be used as a textbook for a special topic course in computer science. It addresses contemporary research topics of interest such as intelligent control, genetic algorithms, neural networks, optimization techniques, expert system
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THEORY AND DECISION LIBRARY
General Editors: W. Leinfellner (Vienna) and G. Eberlein (Munich) Series A: Philosophy and Methodology of the Social Sciences Series B: Mathematical and Statistical Methods Series C: Game Theory, Mathematical Programming and Operations Research
SERIES B: MATHEMATICAL AND STATISTICAL METHODS VOLUME 38
Editor: H. J. Skala (Paderborn); Assistant Editor: M. Kraft (paderborn); Editorial Board: J. Aczel (Waterloo, Ont.), G. Bamberg (Augsburg), H. Drygas (Kassel), W. Eichhorn (Karlsruhe), P. Fishburn (Murray Hill, N.J.), D. Fraser (Toronto), W. Janko (Vienna), P. de Jong (Vancouver), T. Kariya (Tokyo), M. Machina (La Jolla, Calif.), A. Rapoport (Toronto), M. Richter (Kaiserslautern), B. K. Sinha (Cattonsville, Md.), D. A. Sprott (Waterloo, Ont.), P. Suppes (Stanford, Calif.), H. Theil (St. Augustine, Fla.), E. Trillas (Madrid), L. A. Zadeh (Berkeley, Calif.).
Scope: The series focuses on the application of methods and ideas of logic, mathematics and statistics to the social sciences. In particular, formal treatment of social phenomena, the analysis of decision making, information theory and problems of inference will be central themes of this part of the library. Besides theoretical results, empirical investigations and the testing of theoretical models of real world problems will be subjects of interest. In addition to emphasizing interdisciplinary communication, the series will seek to support the rapid dissemination of recent results.
APPLICATIONS OF CONTINUOUS MATHEMATICS TO COMPUTER SCIENCE by
HUNG T. NGUYEN New Mexico State University, Las Cruces, New Mexico, U.S.A.
and
VLADIK KREINOVICH University of Texas at El Paso, El Paso, Texas, U.S.A.
SPRINGER-SCIENCE+BUSINESS MEDIA, B.V.
A C.I.P. Catalogue record for this book is available from the Library of Congress
ISBN 978-90-481-4901- 8 DOI 10.1007/978-94-017-0743-5
ISBN 978-94-017-0743-5 (eBook)
Printed on acid-free paper
AU Rights Reserved © 1997 Springer Science+Business Media Dordrecht Originally published by Kluwer Academic Publishers in 1997
No part of the material protected by this copyright notice may be reproduced or utilized in any form or by any means, electronic ormechanical, inc1uding photocopying, recording or by any information storage and retrieval syst~m, without written permis sion from the copyright owner.
CONTENTS
PREFACE 1
IX
ALGORITHM COMPLEXITY: TWO SIMPLE EXAMPLES
1
SOLVING GENERAL LINEAR FUNCTIONAL EQUATIONS: AN APPLICATION TO ALGORITHM COMPLEXITY
21
3
PROGRAM TESTING: A PROBLEM
45
4
OPTIMAL PROGRAM TESTING
65
5
OPTIMAL CHOICE OF A PENALTY FUNCTION: SIMPLEST CASE OF ALGORITHM DESIGN
87
SOLVING GENERAL LINEAR DIFFERENTIAL EQUATIONS WITH CONSTANT COEFFICIENTS: AN APPLICATION TO CONSTRAINED OPTIMIZATION
109
SIMULATED ANNEALING: "SMOOTH" (LOCAL) DISCRETE OPTIMIZATION
131
2
6
7
v
VI
8
9
ApPLICATIONS OF CONTINUOUS MATHEMATICS
GENETIC ALGORITHMS: "NON-SMOOTH" DISCRETE OPTIMIZATION
153
RISC COMPUTER ARCHITECTURE AND INTERNET GROWTH: TWO APPLICATIONS OF EXTRAPOLATION
175
10
