Computability Theory

An Introduction

Neil D. Jones, Robert L. Ashenhurst

• Publisher: Academic Press
• Year: 2014
• ISBN:
  9781483218489
• Topic: Mathematics
• Subtopic: Mathematics General
• Index: Mathematics

Computability Theory: An Introduction provides information pertinent to the major concepts, constructions, and theorems of the elementary theory of computability of recursive functions. This book provides mathematical evidence for the validity of the Church–Turing thesis. Organized into six chapters, this book begins with an overview of the concept of effective process so that a clear understanding of the effective computability of partial and total functions is obtained. This text then introduces a formal development of the equivalence of Turing machine computability, enumerability, and decidability with other formulations. Other chapters consider the formulas of the predicate calculus, systems of recursion equations, and Post's production systems. This book discusses as well the fundamental properties of the partial recursive functions and the recursively enumerable sets. The final chapter deals with different formulations of the basic ideas of computability that are equivalent to Turing-computability. This book is a valuable resource for undergraduate or graduate students.

Table of contents

• Front Cover
• Computability Theory: An Introduction
• Copyright Page
• Table of Contents
• PREFACE
• LIST OF SPECIAL SYMBOLS
• CHAPTER I. MATHEMATICAL BASIS
• CHAPTER Il. INTRODUCTION TO COMPUTABILITY
• CHAPTER Ill. DESCRIPTION OF TURINGMACHINES BY PREDICATES
• CHAPTER IV. DECISION OF PREDICATES BY TURING MACHINES
• CHAPTER V. THE NORMAL FORM THEOREMS AND CONSEQUENCES
• CHAPTER VI. OTHER FORMULATIONS OF COMPUTABILITY
• REFERENCES
• INDEX