What can computers do in principle? What are their inherent
theoretical limitations? These are questions to which computer
scientists must address themselves. The theoretical framework which
enables such questions to be answered has been developed over the
last fifty years from the idea of a computable function:
intuitively a function whose values can be calculated in an
effective or automatic way. This book is an introduction to
computability theory (or recursion theory as it is traditionally
known to mathematicians). Dr Cutland begins with a mathematical
characterisation of computable functions using a simple idealised
computer (a register machine); after some comparison with other
characterisations, he develops the mathematical theory, including a
full discussion of non-computability and undecidability, and the
theory of recursive and recursively enumerable sets. The later
chapters provide an introduction to more advanced topics such as
Gildel's incompleteness theorem, degrees of unsolvability, the
Recursion theorems and the theory of complexity of computation.
Computability is thus a branch of mathematics which is of relevance
also to computer scientists and philosophers. Mathematics students
with no prior knowledge of the subject and computer science
students who wish to supplement their practical expertise with some
theoretical background will find this book of use and interest.
General
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