**Author**: Hans F. de Groote

**Publisher:** Springer Science & Business Media

**ISBN:**

**Category:** Computers

**Page:** 135

**View:** 414

The notion of complexity is an important contribution of logic to theoretical computer science and mathematics. This volume attempts to approach complexity in a holistic way, investigating mathematical properties of complexity hierarchies at the same time as discussing algorithms and computational properties. A main focus of the volume is on some of the new paradigms of computation, among them Quantum Computing and Infinitary Computation. The papers in the volume are tied together by an introductory article describing abstract properties of complexity hierarchies. This volume will be of great interest to both mathematical logicians and theoretical computer scientists, providing them with new insights into the various views of complexity and thus shedding new light on their own research.

This first part presents chapters on models of computation, complexity theory, data structures, and efficient computation in many recognized sub-disciplines of Theoretical Computer Science.

The algorithmic solution of problems has always been one of the major concerns of mathematics. For a long time such solutions were based on an intuitive notion of algorithm. It is only in this century that metamathematical problems have led to the intensive search for a precise and sufficiently general formalization of the notions of computability and algorithm. In the 1930s, a number of quite different concepts for this purpose were pro posed, such as Turing machines, WHILE-programs, recursive functions, Markov algorithms, and Thue systems. All these concepts turned out to be equivalent, a fact summarized in Church's thesis, which says that the resulting definitions form an adequate formalization of the intuitive notion of computability. This had and continues to have an enormous effect. First of all, with these notions it has been possible to prove that various problems are algorithmically unsolvable. Among of group these undecidable problems are the halting problem, the word problem theory, the Post correspondence problem, and Hilbert's tenth problem. Secondly, concepts like Turing machines and WHILE-programs had a strong influence on the development of the first computers and programming languages. In the era of digital computers, the question of finding efficient solutions to algorithmically solvable problems has become increasingly important. In addition, the fact that some problems can be solved very efficiently, while others seem to defy all attempts to find an efficient solution, has called for a deeper under standing of the intrinsic computational difficulty of problems.

This little book is conceived as a service to mathematicians attending the 1998 International Congress of Mathematicians in Berlin. It presents a comprehensive, condensed overview of mathematical activity in Berlin, from Leibniz almost to the present day (without, however, including biographies of living mathematicians). Since many towering figures in mathematical history worked in Berlin, most of the chapters of this book are concise biographies. These are held together by a few survey articles presenting the overall development of entire periods of scientific life at Berlin. Overlaps between various chapters and differences in style between the chap ters were inevitable, but sometimes this provided opportunities to show different aspects of a single historical event - for instance, the Kronecker-Weierstrass con troversy. The book aims at readability rather than scholarly completeness. There are no footnotes, only references to the individual bibliographies of each chapter. Still, we do hope that the texts brought together here, and written by the various authors for this volume, constitute a solid introduction to the history of Berlin mathematics.

This book constitutes the refereed proceedings of the 28th International Colloquium on Automata, Languages and Programming, ICALP 2001, held in Crete, Greece in July 2001. four invited papers were carefully reviewed and selected from a total of 208 submissions. complexity, algorithm analysis, approximation and optimization, complexity, concurrency, efficient data structures, graph algorithms, language theory, codes and automata, model checking and protocol analysis, networks and routing, reasoning and verification, scheduling, secure computation, specification and deduction, and structural complexity.

Here Professor Paterson brings together papers from the 1990 Durham symposium on Boolean function complexity. The participants include many well known figures in the field.

Table of Contents: D. Duffie: Martingales, Arbitrage, and Portfolio Choice • J. Fröhlich: Mathematical Aspects of the Quantum Hall Effect • M. Giaquinta: Analytic and Geometric Aspects of Variational Problems for Vector Valued Mappings • U. Hamenstädt: Harmonic Measures for Leafwise Elliptic Operators Along Foliations • M. Kontsevich: Feynman Diagrams and Low-Dimensional Topology • S.B. Kuksin: KAM-Theory for Partial Differential Equations • M. Laczkovich: Paradoxical Decompositions: A Survey of Recent Results • J.-F. Le Gall: A Path-Valued Markov Process and its Connections with Partial Differential Equations • I. Madsen: The Cyclotomic Trace in Algebraic K-Theory • A.S. Merkurjev: Algebraic K-Theory and Galois Cohomology • J. Nekovár: Values of L-Functions and p-Adic Cohomology • Y.A. Neretin: Mantles, Trains and Representations of Infinite Dimensional Groups • M.A. Nowak: The Evolutionary Dynamics of HIV Infections • R. Piene: On the Enumeration of Algebraic Curves - from Circles to Instantons • A. Quarteroni: Mathematical Aspects of Domain Decomposition Methods • A. Schrijver: Paths in Graphs and Curves on Surfaces • B. Silverman: Function Estimation and Functional Data Analysis • V. Strassen: Algebra and Complexity • P. Tukia: Generalizations of Fuchsian and Kleinian Groups • C. Viterbo: Properties of Embedded Lagrange Manifolds • D. Voiculescu: Alternative Entropies in Operator Algebras • M. Wodzicki : Algebraic K-Theory and Functional Analysis • D. Zagier: Values of Zeta Functions and Their Applications

Digital Signal Processing: Applications to Communications and Algebraic Coding Theories discusses the design of computationally efficient digital signal processing algorithms over finite fields and the relation of these algorithms to algebraic error-correcting codes. The book provides chapters that cover such topics as signal processing techniques employed for modeling, synthesis, and analysis; systems of bilinear forms; efficient finite field algorithms; the design and study of long length cyclic convolutions and some preliminary results on their relation to linear codes; the study of the algebraic structure of the class of linear codes obtained from bilinear cyclic and aperiodic convolution algorithms over the finite field of interest; and the concept of a generalized hybrid Automatic- Repeat-Request (ARQ) scheme for adaptive error control in digital communication systems. Engineers, mathematicians, and computer scientists will find the text invaluable.

This book constitutes the refereed proceedings of the 18th Annual Symposium on Theoretical Aspects of Computer Science, STACS 2001, held in Dresden, Germany in February 2001. The 46 revised full papers presented together with three invited papers were carefully reviewed and selected from a total of 153 submissions. The papers address foundational aspects from all current areas of theoretical computer science including algorithms, data structures, automata, formal languages, complexity, verification, logic, graph theory, optimization, etc.

This book constitutes the proceedings of the 11th International Conference on Applied Algebra, Algebraic Algorithms and Error-Correcting Codes, AAECC-11, held in Paris, France in July 1995. The volume presents five invited papers and 32 full revised research papers selected from a total of 68 submissions; it is focussed on research directed to the exploitation of algebraic techniques and methodologies for the application in coding and computer algebra. Among the topics covered are coding, cryptoloy, communication, factorization of polynomials, Gröbner bases, computer algebra, algebraic algorithms, symbolic computation, algebraic manipulation.

Symposium on Algorithms (ESA '93), held in Bad Honnef, near Boon, in Germany, September 30 - October 2, 1993. The symposium is intended to launchan annual series of international conferences, held in early fall, covering the field of algorithms. Within the scope of the symposium lies all research on algorithms, theoretical as well as applied, that is carried out in the fields of computer science and discrete applied mathematics. The symposium aims to cater to both of these research communities and to intensify the exchange between them. The volume contains 35 contributed papers selected from 101 proposals submitted in response to the call for papers, as well as three invited lectures: "Evolution of an algorithm" by Michael Paterson, "Complexity of disjoint paths problems in planar graphs" by Alexander Schrijver, and "Sequence comparison and statistical significance in molecular biology" by Michael S. Waterman.

The present volume contains the proceedings of the AAECC-5 Conference held at Menorca (Balearic Islands), June 15-19, 1987. The annual International AAECC Conference covers a range of topics related to Applied Algebra, Error-Correcting Codes, Finite Algebraic Structures, Computational Methods and Complexity in Algebra and Geometry. For the AAECC-5 Conference 73 papers were presented. Out of these thirty papers were selected for publication in the proceedings. They deal with topics such as error correcting codes (concerning problems of covering radius, decoding methods, expert systems and general results in coding theory), computational algebra, Gröbner basis, complexity, finite algebra and graphs. The proceedings of the 6th conference are published as Vol. 357 of the Lecture Notes in Computer Science.

Aerodynamics and hydrodynamics are still the main domains that make greater use of flow visualization and classical optical techniques such as schlieren and interferometry than of more recent techniques such as holography speckle, laser light sheets, laser-induced tracers and laser-induced fluorescence. A number of studies are now under way on turbulent and vortex flows, within boundary layers or wakes, in the mixing layer of two flows. Other studies concern jets, two-phase flows and air-water interface. To review and discuss developments in flow visualization, four international symposia have been held. Following Tokyo, Bochum and Ann Arbor, the Fourth International Symposium on Flow Visualization (ISFV 4) was held in Paris in August 1986.

Now in its third edition, this highly successful textbook is widely regarded as the 'bible of computer algebra'.

The 1st International Conference on Supercomputing took place in Athens, Greece, June 8-12, 1987. The purpose of this conference was to bring together researchers from universities, industrial laboratories, and other research institutions with common interests in architectures and hardware technology, software, and applications for supercomputers. Authors from 12 countries submitted 107 papers, from which 52 were accepted and presented at the conference. In addition, 15 distinguished researchers presented invited papers. The papers from these presentations make up the current proceedings volume. Based on the quality of the papers presented and the response and excitement of the participants, the Program Committee has decided to hold annual meetings on the subject of supercomputing.

This volume contains the proceedings of the 8th Conference on Foundations of Software Technology and Theoretical Computer Science held in Pune, India, on December 21-23, 1988. This internationally well-established Indian conference series provides a forum for actively investigating the interface between theory and practice of Software Science. It also gives an annual occasion for interaction between active research communities in India and abroad. Besides attractive invited papers the volume contains carefully reviewed submitted papers on the following topics: Automata and Formal Languages, Graph Algorithms and Geometric Algorithms, Distributed Computing, Parallel Algorithms, Database Theory, Logic Programming, Programming Methodology, Theory of Algorithms, Semantics and Complexity.