A Programming Approach to Computability

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

Part of the Texts and Monographs in Computer Science book series (MCS)

Table of contents

  1. Front Matter
    Pages i-viii
  2. A. J. Kfoury, Robert N. Moll, Michael A. Arbib
    Pages 1-16
  3. A. J. Kfoury, Robert N. Moll, Michael A. Arbib
    Pages 17-44
  4. A. J. Kfoury, Robert N. Moll, Michael A. Arbib
    Pages 45-74
  5. A. J. Kfoury, Robert N. Moll, Michael A. Arbib
    Pages 75-94
  6. A. J. Kfoury, Robert N. Moll, Michael A. Arbib
    Pages 95-137
  7. A. J. Kfoury, Robert N. Moll, Michael A. Arbib
    Pages 138-151
  8. A. J. Kfoury, Robert N. Moll, Michael A. Arbib
    Pages 152-175
  9. A. J. Kfoury, Robert N. Moll, Michael A. Arbib
    Pages 176-195
  10. A. J. Kfoury, Robert N. Moll, Michael A. Arbib
    Pages 196-234
  11. Back Matter
    Pages 235-253

About this book

Introduction

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.

Keywords

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

Authors and affiliations

  • A. J. Kfoury
    • 1
  • Robert N. Moll
    • 2
  • Michael A. Arbib
    • 2
  1. 1.Department of MathematicsBoston UniversityBostonUSA
  2. 2.Department of Computer and Information ScienceUniversity of MassachusettsAmherstUSA

Bibliographic information

  • DOI https://doi.org/10.1007/978-1-4612-5749-3
  • Copyright Information Springer-Verlag New York 1982
  • Publisher Name Springer, New York, NY
  • eBook Packages Springer Book Archive
  • Print ISBN 978-1-4612-5751-6
  • Online ISBN 978-1-4612-5749-3
  • Series Print ISSN 0172-603X
  • About this book