Computability

This survey of computability theory provides techniques and tools for mathematically analyzing computational processes and investigating theoretical limitations of computing, covering basic theory, advanced chapters, and various classes of computable functionals.

Format: Paperback
Publication date: 03 August 2023
Publisher: Springer International Publishing

Computability theory is a branch of mathematics that studies the mathematical foundations of computing. It provides techniques and tools for mathematically analyzing computational processes and investigating their theoretical limitations. The textbook begins with an introduction to the mathematisation of "mechanical process" using URM programs, which explains basic theory such as primitive recursive functions and predicates, sequence-coding, partial recursive functions and predicates, and loop programs. Advanced chapters cover the Ackerman function, Tarski's theorem on the non-representability of truth, Gödel's incompleteness and Rosser's incompleteness theorems, two short proofs of the incompleteness theorem based on Lob's deliverability conditions, Church's thesis, the second recursion theorem and applications, a provably recursive universal function for the primitive recursive functions, Oracle computations and various classes of computable functionals, the Arithmetical hierarchy, Turing reducibility and Turing degrees and the priority method, a thorough exposition of various versions of the first recursive theorem, Blum's complexity, Hierarchies of primitive recursive functions, and a machine-independent characterisation of Cobham's feasibly computable functions.

ISBN-13: 9783030832049