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Theories of computational complexity
Title:
Theories of computational complexity
Author:
Calude, Cristian, 1952-
ISBN:
9780444703569
9780080867755
9781281793133
9786611793135
Personal Author:
Publication Information:
Amsterdam ; New York : North-Holland ; New York, N.Y., U.S.A. : Sole distributors for the U.S.A. and Canada, Elsevier Science Pub. Co., 1988.
Physical Description:
1 online resource (xiii, 487 pages).
Series:
Annals of discrete mathematics ; 35
Annals of discrete mathematics ; 35.
General Note:
Includes indexes.
Contents:
Front Cover; Theories of Computational Complexity; Copyright Page; Contents; Preface; Introduction; Chapter 1; 1. Primitive Recursive Hierarchies; 1.1. Examples; 1.2. Ackermann-Peter's Hierarchy; 1.3. Primitive Recursive Functions; 1.4. Primitive Recursive Invariants; 1.5. Primitive Recursive Enumerations; 1.6. Sudan's Hierarchy; 1.7. Universal Sequences of Primitive Recursive Functions; 1.8. Primitive Recursive String-functions; 1.9. History; 1.10. Exercises and Problem; Chapter 2; 2. Recursive Functions; 2.1. Examples; 2.2. Arithmetization of Computation: An Example
2.3. Equational Characterization of Partial Recursive Functions2.4. GODEL Numberings; 2.5. Recursively Enumerable Sets; 2.6. Undecidability and Independence; 2.7. Uniformity; 2.8. Operators; 2.9. Recursive Real Numbers; 2.10. History; 2.11. Exercises and Problems; Chapter 3; 3. BLUM's Complexity Theory; 3.1. Examples; 3.2. BLUM Spaces; 3.3. Recursive Dependence of Complexity Measures; 3.4. Complexity Classes; 3.5. The Speed-up Phenomenon; 3.6. The Union Theorem; 3.7. Hard Recursive Functions; 3.8. Complexity Sequences; 3.9. A Topological Analysis; 3.10. History; 3.11. Exercises and Problems
Chapter 44. KOLMOGOROV and MARTIN-LOF's Complexity Theory; 4.1. Examples; 4.2. KOLMOGOROV's Complexity; 4.3. MARTIN-LOF Tests; 4.4. Undecidability Theorems; 4.5. Representability Theorems; 4.6. Recursive MARTIN-LOF Tests; 4.7. Infinite Oscillations; 4.8. Probabilistic Algorithms; 4.9. History; 4.10. Exercises and Problems; Chapter 5; 5. Subrecursive Programming Hierarchies; 5.1. Examples; 5.2. The LOOP Language; 5.3. LOOP Hierarchies; 5.4. A Universal Language; 5.5. A Dynamic Characterization of LOOP Classes; 5.6. Augmented LOOP Languages; 5.7. Simple Functions; 5.8. Program Size
5.9. History5.10. Exercises and Problems; Bibliography; Index of notations; Subject index; Author index
Abstract:
This volume presents four machine-independent theories of computational complexity, which have been chosen for their intrinsic importance and practical relevance. The book includes a wealth of results - classical, recent, and others which have not been published before. In developing the mathematics underlying the size, dynamic and structural complexity measures, various connections with mathematical logic, constructive topology, probability and programming theories are established. The facts are presented in detail. Extensive examples are provided, to help clarify notions and constructions. The lists of exercises and problems include routine exercises, interesting results, as well as some open problems.
Genre:
Electronic Access:
Available from ScienceDirect. Online version available for university members only. This requires an institutional login off-campus. ScienceDirect http://www.sciencedirect.com/science/book/9780444703569 ScienceDirect http://www.sciencedirect.com/science/publication?issn=01675060&volume=35 ScienceDirect http://www.sciencedirect.com/science/bookseries/01675060/35 ScienceDirect https://www.sciencedirect.com/science/book/9780444703569Available:*
Shelf Number | Item Barcode | Shelf Location | Status |
|---|---|---|---|
| QA267 .C34 1988 EB | 1191091-1001 | Elsevier E-Book Collections | Searching... |
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