# Computability and Decidability

## An Introduction for Students of Computer Science

• Jacques Loeckx
Textbook

Part of the Lecture Notes in Economics and Mathematical Systems book series (LNE, volume 68)

1. Front Matter
Pages I-VI
2. Jacques Loeckx
Pages 1-10
3. Jacques Loeckx
Pages 11-22
4. Jacques Loeckx
Pages 23-44
5. Jacques Loeckx
Pages 45-49
6. Jacques Loeckx
Pages 50-57
7. Jacques Loeckx
Pages 58-70
8. Back Matter
Pages 71-77

### Introduction

The present Lecture Notes evolved from a course given at the Technische Hogeschool Eindhoven and later at the Technische Hogeschool Twente. They are intended for computer science students; more specifically, their goal is to introduce the notions of computability and decidability, and to prepare for the study of automata theory, formal language theory and the theory of computing. Except for a general mathematical background no preliminary knowledge is presupposed, but some experience in programming may be helpful. While classical treatises on computability and decidability are oriented towards the foundation of mathematics or mathematical logic, the present notes try to relate the subject to computer science. Therefore, the expose is based on the use of strings rather than on that of natural numbers; the notations are similar to those in use in automata theory; in addition, according to a common usage in formal language theory, most of the proofs of computability are reduced to the semi-formal description of a procedure the constructivity of which is apparent to anybody having some programming experience. Notwithstanding these facts the subject is treated with mathematical rigor; a great number of informal comments are inserted in order to allow a good intuitive understanding. I am indebted to all those who drew my attention to some errors and ambiguities in a preliminary version of these Notes. I want also to thank Miss L.A. Krukerink for her diligence in typing the manuscript.

### Keywords

Decidability computability computer computer science logic sets

#### Authors and affiliations

• Jacques Loeckx
• 1
1. 1.Institut für InformatikUniversität des Saarlandes66 SaarbrückenGermany

### Bibliographic information

• DOI https://doi.org/10.1007/978-3-642-80689-6
• Copyright Information Springer-Verlag Berlin Heidelberg 1972
• Publisher Name Springer, Berlin, Heidelberg
• eBook Packages
• Print ISBN 978-3-540-05869-4
• Online ISBN 978-3-642-80689-6
• Series Print ISSN 0075-8442
• Buy this book on publisher's site
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