A Programming Approach to Computability

1. Front Matter

   Pages i-viii

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2. Introduction

   • A. J. Kfoury, Robert N. Moll, Michael A. Arbib

   Pages 1-16

3. The Syntax and Semantics of while-Programs

   • A. J. Kfoury, Robert N. Moll, Michael A. Arbib

   Pages 17-44

4. Enumeration and Universality of the Computable Functions

   • A. J. Kfoury, Robert N. Moll, Michael A. Arbib

   Pages 45-74

5. Techniques of Elementary Computability Theory

   • A. J. Kfoury, Robert N. Moll, Michael A. Arbib

   Pages 75-94

6. Program Methodology

   • A. J. Kfoury, Robert N. Moll, Michael A. Arbib

   Pages 95-137

7. The Recursion Theorem and Properties of Enumerations

   • A. J. Kfoury, Robert N. Moll, Michael A. Arbib

   Pages 138-151

8. Computable Properties of Sets (Part 1)

   • A. J. Kfoury, Robert N. Moll, Michael A. Arbib

   Pages 152-175

9. Computable Properties of Sets (Part 2)

   • A. J. Kfoury, Robert N. Moll, Michael A. Arbib

   Pages 176-195

10. Alternative Approaches to Computability

    • A. J. Kfoury, Robert N. Moll, Michael A. Arbib

    Pages 196-234

11. Back Matter

    Pages 235-253

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Computability theory is at the heart of theoretical computer science. Yet, ironically, many of its basic results were discovered by mathematical logicians prior to the development of the first stored-program computer. As a result, many texts on computability theory strike today's computer science students as far removed from their concerns. To remedy this, we base our approach to computability on the language of while-programs, a lean subset of PASCAL, and postpone consideration of such classic models as Turing machines, string-rewriting systems, and p. -recursive functions till the final chapter. Moreover, we balance the presentation of un solvability results such as the unsolvability of the Halting Problem with a presentation of the positive results of modern programming methodology, including the use of proof rules, and the denotational semantics of programs. Computer science seeks to provide a scientific basis for the study of information processing, the solution of problems by algorithms, and the design and programming of computers. The last 40 years have seen increasing sophistication in the science, in the microelectronics which has made machines of staggering complexity economically feasible, in the advances in programming methodology which allow immense programs to be designed with increasing speed and reduced error, and in the develop­ ment of mathematical techniques to allow the rigorous specification of program, process, and machine.

• Berechenbarkeit
• Programmierung (EDV)
• algorithms
• classification
• computability theory
• formal language
• programming

• Department of Mathematics, Boston University, Boston, USA

  A. J. Kfoury

• Department of Computer and Information Science, University of Massachusetts, Amherst, USA

  Robert N. Moll, Michael A. Arbib

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