Broad in coverage, mathematically sophisticated, and up to date, this book provides an introduction to theories of computability. It treats not only "the" theory of computability (the theory created by Alan Turing and others in the 1930s), but also a variety of other theories (of Boolean functions, automata and formal languages) as theories of computability. These are addressed from the classical perspective of their generation by grammars and from the more modern perspective as rational cones. The treatment of the classical theory of computable functions and relations takes the form of a tour through basic recursive function theory, starting with an axiomatic foundation and developing the essential methods in order to survey the most memorable results of the field. This authoritative account, written by one of the leading lights of the subject, will be required reading for graduate students and researchers in theoretical computer science and mathematics.
"The author is extremely precise and meticulous, giving as much care to a proof that any context-free language can be generated by a grammar in Greibach normal form (GNF) as to a priority argument." Computing Reviews "...an excellent textbook for a beginning researcher who wants to familiarize himself/herself with several axiomatic frameworks for the theory of computability...I enjoyed the nuggets of wit spread throughout the book, providing a pleasant contrast to the abstract material." SIGACT News "Aiming readers at the frontier of research, the book has a point to make, and it makes it in an elegant and attractive way." Mathematical Reviews "The book, which has a list of about 200 references, is well indexed, well organized, and quite well written. But the strongest commendation is for its selection of material and its coherent organization." Siam Review