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An Overview of the Theory of Computational Complexity

An Overview of the Theory of Computational Complexity An Overview of the Theory of Computational Complexity J. HARTMANIS AND J. E. HOPCROFT Cornell University,* Ithaca, New York ABSTRACT. The purpose of this paper is to outline the theory of computational complexity which has emerged as a comprehensive theory during the last decade. This theory is concerned with the quantitative aspects of computations and its central theme is the measuring of the difficulty of computing functions. The paper concentrates on the study of computational complexity measures defined for all computable functions and makes no attempt to survey the whole field exhaustively nor to present the material in historical order. Rather it presents the basic concepts, results, and techniques of computational complexity from a new point of view from which the ideas are more easily understood and fit together as a coherent whole. KEY WORDS AND PHRASES: computational complexity, complexity axioms, complexity measures, computation speed, time-bounds, tape-bounds, speed-up, Turing machines, diagonalization, length of programs 5.20, 5.22, 5.23, 5.24 CR C A T E G O R I E S : 1. Introduction I t is clear that a viable theory of computation must deal realistically with the quantitative aspects of computing and must develop a general theory which http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Journal of the ACM (JACM) Association for Computing Machinery

An Overview of the Theory of Computational Complexity

Journal of the ACM (JACM) , Volume 18 (3) – Jul 1, 1971

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References (49)

Publisher
Association for Computing Machinery
Copyright
Copyright © 1971 by ACM Inc.
ISSN
0004-5411
DOI
10.1145/321650.321661
Publisher site
See Article on Publisher Site

Abstract

An Overview of the Theory of Computational Complexity J. HARTMANIS AND J. E. HOPCROFT Cornell University,* Ithaca, New York ABSTRACT. The purpose of this paper is to outline the theory of computational complexity which has emerged as a comprehensive theory during the last decade. This theory is concerned with the quantitative aspects of computations and its central theme is the measuring of the difficulty of computing functions. The paper concentrates on the study of computational complexity measures defined for all computable functions and makes no attempt to survey the whole field exhaustively nor to present the material in historical order. Rather it presents the basic concepts, results, and techniques of computational complexity from a new point of view from which the ideas are more easily understood and fit together as a coherent whole. KEY WORDS AND PHRASES: computational complexity, complexity axioms, complexity measures, computation speed, time-bounds, tape-bounds, speed-up, Turing machines, diagonalization, length of programs 5.20, 5.22, 5.23, 5.24 CR C A T E G O R I E S : 1. Introduction I t is clear that a viable theory of computation must deal realistically with the quantitative aspects of computing and must develop a general theory which

Journal

Journal of the ACM (JACM)Association for Computing Machinery

Published: Jul 1, 1971

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