Theory of Recursive Functions and Effective Computability

Rating:
Summary: Good reference
Review: I looked long and hard for a reference in recursion theory and this was the only one which was acceptable. Luckily it is also quite good.

Most books in the subject either introduce the material in their own non-standard notation which, while suitable for a survey course in the material is of little help when attempting to actually read papers in the field. These books are also usually very basic ignoring things like the arithmetical hierarchy. Other books in this subject seem to mostly be advanced texts and don't cover, or cover very briefly, the important theorems.

This book starts at turing machines and recursive functions. Going through the basic results like the halting problem and rapidly moving on to more advanced topics like creative sets, cylinders and hypersimple sets. Posts problem(with Friedberg's solution) and the fixed point theorem are covered as well. The final part of the book covers degrees of unsolvability arithmetical hierarchy and the analytic hierarchy.

While the book does cover recursive fucntions and turing machines I would suggest previous experience with them before reading as the coverage is brief and doesn't give the reader a feeling of how these systems work.

If you are taking a class in the subject or want to understand modern recursion theory this is a wonderful place to start.

Rating:
Summary: Good reference
Review: I looked long and hard for a reference in recursion theory and this was the only one which was acceptable. Luckily it is also quite good.

Most books in the subject either introduce the material in their own non-standard notation which, while suitable for a survey course in the material is of little help when attempting to actually read papers in the field. These books are also usually very basic ignoring things like the arithmetical hierarchy. Other books in this subject seem to mostly be advanced texts and don't cover, or cover very briefly, the important theorems.

This book starts at turing machines and recursive functions. Going through the basic results like the halting problem and rapidly moving on to more advanced topics like creative sets, cylinders and hypersimple sets. Posts problem(with Friedberg's solution) and the fixed point theorem are covered as well. The final part of the book covers degrees of unsolvability arithmetical hierarchy and the analytic hierarchy.

While the book does cover recursive fucntions and turing machines I would suggest previous experience with them before reading as the coverage is brief and doesn't give the reader a feeling of how these systems work.

If you are taking a class in the subject or want to understand modern recursion theory this is a wonderful place to start.

Rating:
Summary: great book
Review: The definitive book on computabilty and recursive function theory. I remember reading this book in preparation for research in complexity theory. I found it very stressful reading the book, but it was a good kind of stress. The kind that forces you to think deeply about what the author is writing about. In addition to the main text, the author provides numerous thought-provoking problems whose study could make a coure unto themselves. I read this book as a 3rd-year graduate student in

math. If you are an undergraduate and are interested in computability theory, I recommend Nigel's Cutland's book on the subject.

Rating:
Summary: A classic!
Review: The definitive book on computabilty and recursive function theory. I remember reading this book in preparation for research in complexity theory. I found it very stressful reading the book, but it was a good kind of stress. The kind that forces you to think deeply about what the author is writing about. In addition to the main text, the author provides numerous thought-provoking problems whose study could make a coure unto themselves. I read this book as a 3rd-year graduate student in

math. If you are an undergraduate and are interested in computability theory, I recommend Nigel's Cutland's book on the subject.

Rating:
Summary: great book
Review: There are a lot of good introductory books on computation theory,
but after reading them you may be left asking "okay, what do
I read next?" Well _this_ is the book. If you're looking for something in between the undergraduate intro books and
the research-level articles then this is for you. It develops recursive function theory in a succinct, mathematically mature manner that is freed from the details of any particular formalism. You should have previous exposure to turing machines and undecidable problems, an appreciation of the defense and use of Church's thesis, and familiarity with basic mathematical logic. Just to be clear, this book is NOT:
-a computer science, programming, or algorithms book
-an introductory book
-a book about automata or weak models of computation (such as regular languages or context-free grammars)
-a complexity theory book (no time bounds or np-completeness etc)