Book 2008

New Computational Paradigms

Changing Conceptions of What is Computable


ISBN: 978-0-387-36033-1 (Print) 978-0-387-68546-5 (Online)

Table of contents (20 chapters)

  1. Front Matter

    Pages i-xiii

  2. The Turing Model of Computation and its Applications to Logic, Mathematics, Philosophy, and Computer Science

    1. Chapter

      Pages 3-15

      Alan Turing, Logical and Physical

    2. Chapter

      Pages 19-34

      Computability and Numberings

    3. Chapter

      Pages 35-58

      Computation as Conversation

    4. Chapter

      Pages 59-85

      Computation Paradigms in Light of Hilbert's Tenth Problem

    5. Chapter

      Pages 87-118

      Elementary Algorithms and Their Implementations

    6. Chapter

      Pages 119-138

      Applications of the Kleene–Kreisel Density Theorem to Theoretical Computer Science

    7. Chapter

      Pages 139-152

      Church Without Dogma: Axioms for Computability

    8. Chapter

      Pages 153-194

      Computability on Topological Spaces via Domain Representations

    9. Chapter

      Pages 195-209

      On the Power of Broadcasting in Mobile Computing

  3. Logic, Algorithms and Complexity

    1. Chapter

      Pages 213-222

      The Computational Power of Bounded Arithmetic from the Predicative Viewpoint

    2. Chapter

      Pages 223-258

      Effective Uniform Bounds from Proofs in Abstract Functional Analysis

    3. Chapter

      Pages 259-285

      Effective Fractal Dimension in Algorithmic Information Theory

    4. Chapter

      Pages 287-312

      Metamathematical Properties of Intuitionistic Set Theories with Choice Principles

    5. Chapter

      Pages 313-340

      New Developments in Proofs and Computations

  4. Models of Computation from Nature

    1. Chapter

      Pages 343-371

      From Cells to (Silicon) Computers, and Back

    2. Chapter

      Pages 373-379

      Computer Science, Informatics, and Natural Computing—Personal Reflections

  5. Computable Analysis and Real Computation

    1. Chapter

      Pages 383-423

      A Survey on Continuous Time Computations

    2. Chapter

      Pages 425-491

      A Tutorial on Computable Analysis

    3. Chapter

      Pages 493-519

      A Continuous Derivative for Real-Valued Functions

    4. Chapter

      Pages 521-557

      Infinite Time Computable Model Theory

  6. Back Matter

    Pages 559-559