- Paperback: 506 pages
- Publisher: The MIT Press (April 22, 1987)
- Language: English
- ISBN-10: 0262680521
- ISBN-13: 978-0262680523
- Product Dimensions: 6 x 1 x 9 inches
- Shipping Weight: 1.7 pounds (View shipping rates and policies)
- Average Customer Review: 4.5 out of 5 stars See all reviews (10 customer reviews)
- Amazon Best Sellers Rank: #1,333,249 in Books (See Top 100 in Books)
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Theory of Recursive Functions and Effective Computability Paperback – April 22, 1987
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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.
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)
math. If you are an undergraduate and are interested in computability theory, I recommend Nigel's Cutland's book on the subject.
It says no previous logic course is assumed, but you actually need set theory and basic logic from the beginning. Also, coverage of the basics is cursory, so it would help to have done something like Cutland.
Most Recent Customer Reviews
This is a complete and concise presentation of classical mathematical computation theory. As a student, I took a two semester course, taught by S C Kleene, covering this text. Read morePublished 20 months ago by WRightStarr