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Abstract Recursion and Intrinsic Complexity


Part of Lecture Notes in Logic

  • Date Published: December 2018
  • availability: In stock
  • format: Hardback
  • isbn: 9781108415583

£ 95.00

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About the Authors
  • 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 part is suitable for use as a textbook for an advanced undergraduate or graduate course: all the necessary elementary facts from logic, recursion theory, arithmetic and algebra are included. Part II develops and applies an extension of the homomorphism method due jointly to the author and Lou van den Dries for deriving lower complexity bounds for problems in number theory and algebra which (provably or plausibly) restrict all elementary algorithms from specified primitives. The book includes over 250 problems, from simple checks of the reader's understanding, to current open problems.

    • Presents and applies a new framework for the complexity of algorithms
    • Largely self-contained, the book provides all necessary facts from logic, recursion theory, arithmetic and algebra
    • Contains over 250 problems to help the reader get to grips with the material
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    Reviews & endorsements

    '… the author presents basic methods, approaches and results of the theory of abstract (first-order) recursion and its relevance to the foundations of the theory of algorithms and computational complexity …' Marat M. Arslanov, Mathematical Reviews Clippings

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    Product details

    • Date Published: December 2018
    • format: Hardback
    • isbn: 9781108415583
    • length: 250 pages
    • dimensions: 235 x 157 x 18 mm
    • weight: 0.47kg
    • contains: 5 b/w illus. 260 exercises
    • availability: In stock
  • Table of Contents

    1. Preliminaries
    Part I. Abstract (First Order) Recursion:
    2. Recursive (McCarthy) programs
    3. Complexity theory for recursive programs
    Part II. Intrinsic Complexity:
    4. The homomorphism method
    5. Lower bounds from Presburger primitives
    6. Lower bounds from division with remainder
    7. Lower bounds from division and multiplication
    8. Non-uniform complexity in N
    9. Polynomial nullity (0-testing)
    Symbol index
    General index.

  • Author

    Yiannis N. Moschovakis, University of California, Los Angeles
    Yiannis N. Moschovakis is Professor Emeritus and Distinguished Research Professor of Mathematics at the University of California, Los Angeles, and Professor Emeritus at the University of Athens. Among his many professional commendations he is a Fellow of the AMS and a corresponding member of the Academy of Athens. He has received Guggenheim and Sloan Fellowships and has been an invited speaker at the International Congress of Mathematicians. Professor Moschovakis has worked primarily in the theory of recursion, descriptive set theory and the foundations of the theory of algorithms and computation.

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