COMPUTABILITY. An introduction to recursive function theory. NIGEL CUTLAND. Department of Pure Mathematics, University of Hull. CAMBRIDGE. Citation. Enderton, H. B. Review: Nigel Cutland, Computability. An Introduction to Recursive Function Theory. J. Symbolic Logic 52 (), no. 1, CSComputability/Computability,An Introduction To Recursive Function Theory (Cutland).pdf. aa37c96 on Mar 22, @nausicaasnow nausicaasnow init.

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Cutland has produced here an excellent and much needed textbook which will undoubtedly help to establish recursion theory as a more widely taught branch of mainstream mathematics. This introduction to recursive theory computability begins with a mathematical characterization of computable functions, develops the mathematical theory and includes a full discussion of noncomputability and undecidability.

Would you like to tell us about a lower price? If you are a seller for this product, would you like to suggest updates through seller support? 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: 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.

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One of these items ships sooner than the other. Buy the selected items together This item: Ships from and sold by Amazon. Customers who bought this item also bought. Page 1 of 1 Start over Page 1 of 1. Recursively Enumerable Sets and Degrees: The Computabikity of Computation. Cambridge University Press; 1 edition June 30, Language: Try the Kindle edition and experience these great reading features: Share your thoughts with other customers.

## An Introduction to Recursive Function Theory

funtion Write a customer review. Showing of 9 reviews. Top Reviews Most recent Top Reviews. There was a problem filtering reviews right now. Please try again later. One thing I really appreciate about this textbook thru Chapter 7 is that as one progresses thru the the book, it mostly stays at a steady level of abstraction, not becoming much more difficult. Therefore, if a reader can understand the first two chapters, they can probably understand Chapters pretty well. Many of those uses are in proofs of theorems, the worst place for them.

This ann of the URM model also means it is independent of the Chomsky hierarchy of language classes that run on those automata just mentioned. All this makes the URM a very clean single model of computation, which has some strong advantages. By Chapter 5, the text mainly deals with general sets of programs, which gets rid of most of the overt URMishness.

At that point, this becomes a math text on the theory of computing using no particular model of computation. This break at chapter 5 eventually trips us into subjects of regular recursion theory. Then short Chapter 8 is misplaced in the book and also unfamiliar in subject matter to the author, yheory he told us the five older textbooks he used to fake that chapter.

With long Chapter 9, the compytability becomes marginally more difficult than previous chapters to its end with Chapter For this reader, Chapter 9 was unremittingly tedious to read, comoutability completely theoretical treatment, with no linkage at all to good examples of more concrete ‘reductions’ in earlier chapters. Chapter 10 was much more interesting again and somewhat linked back to Chapter 5.

Chapter 11, my final one, was quite unusual in ‘sort of’ getting into anthropology, psychology, and damaging enemy computers in war, inspired by the seemingly quite weak 2nd recursion theorem.

For this intorduction, a reader could just read the highly clarifying remarks at bottom of p. I read this book 12Jun to 30Jul That book is still available from Amazon and appears to be quite difficult, with notably dense page layouts.

Tunction present MIT paperback of the Rogers was a reprinting of the original book on different publisher. For those interested, here is a link to that book: The Rogers text is a quite credible ‘next level’ read for after reading this very good book presently under review.

In fact, I’ve started reading the Hartley Rogers text on Wed 24Jul13, while keeping the Cutland on curland during that read. Clean and clearly written, self-contained. Best for theoy or text book for undergraduates or graduate students.

## Theory of Computability

I think it is very suitable for I think it is very suitable for those who do want to learn something about some basic principle of computer science. This is a well-written book, and gives a satisfying account of the field of recursion theory. It covers basic aspects of recursion theory, Godel numbering, the structure of recursive and recursively enumerable sets, and even a brief and quite sketchy foray into complexity results at the end.

It is, however, worth deciding whether you are in the target audience before making a purchase. If you are trying to make a thery transition over into theory topics from, say, a career of practical software development tasks, then this is the wrong book.

Try Sipser’s Introduction to the Theory of Computation instead. Sipser is more willing to spend time on demonstrating the intuitive picture, and relies less on formal mathematical arguments. This book can come later to fill in some of the mathematical properties. On the opposite funxtion of the spectrum, this is a passable but mediocre reference book for recursion theory.

It omits major topics, such as the arithmetic hierarchy. It deviates considerably from other traditional treatments. These decisions will get annoying if you plan to read bits and pieces rather than learn in sequence according to the author’s presentation. Buy this book if you are in the middle.

It’s a great book if you’ve funcion some decidability results, but not a formal mathematical treatment; and if you intend to follow the book and learn what it decides rather than look up specific topics. In that situation, it’s hard to see how you could do better. This introduction for undergrads assumes no specifics other than general experience in college math. The writing is clear and exercises are interspersed and follow naturally from the explanations. Proofs are explanatory and easy to follow, though often rather informal.

However, it looses some of its best qualities about halfway through the book. The early chapters give excellent context and motivation, but by chapter 4 that is mostly gone.

It introductiln that the push to cover more topics is what led to making the introduction of new topics more and more brief. The later chapters give little feeling for how it all fits together and why we should care. You can look up the same topics in Rogers or Odifreddi to get an idea of the interesting things that could have been said.

If you are a computer scientist who would like to delve into the foundations of computing for the first time, this is the perfect book for you. The author uses unlimited register machines as his computing model, then shows equivalence with this model and other modelssuch as the Turing machine.

The reader should find more advanced topics, such Godel’s Incompleteness Theorem, the Recursion Theorem’s, and Reducibility to be computabilify accessible. When I first read this book I thought some of the parts elementary, but comparing it to the above text I realized it was doing the job of teaching by giving good illustrations of the processes involved.

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### Theory of Computability

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