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Abstract Recursion and Intrinsic Complexity

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This book presents and applies a framework for studying the complexity of algorithms. It is aimed at logicians, computer scientists, mathematicians and philosophers interested in the theory of computation and its foundations, and it is written at a level suitable for non-specialists. Part I provides an accessible introduction to abstract recursion theory and its connection with computability and complexity. This  Read more...

Author(s): Yiannis N. Moschovakis
Series: Lectures Notes in Logic 48
Publisher: Cambridge University Press / Association for Symbolic Logic
Year: 2019

Language: English
Pages: 0
Tags: Recursion theory;Induction (Mathematics)

Abstract......Page 1
Title page......Page 3
Contents......Page 5
Introduction......Page 9
1. Preliminaries......Page 15
Part I. Abstract (first order) recursion......Page 55
2. Recursive (McCarthy) programs......Page 57
3. Complexity theory for recursive programs......Page 111
Part II. Intrinsic complexity......Page 135
4. The homomorphism method......Page 137
5. Lower bounds from Presburger primitives......Page 167
6. Lower bounds from division with remainder......Page 179
7. Lower bounds from division and multiplication......Page 199
8. Non-uniform complexity in ℕ......Page 211
9. Polynomial nullity (0-testing)......Page 217
References......Page 237
Symbol index......Page 245
General index......Page 247