George Tourlakis
Computability
Computability
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- More about Computability
This survey of computability theory provides techniques and tools to analyze computational processes and investigate theoretical limitations, covering basic theory, advanced topics, and applications.
Format: Hardback
Length: 637 pages
Publication date: 03 August 2022
Publisher: Springer Nature Switzerland AG
This comprehensive survey of computability theory provides computer scientists, mathematicians, and philosophers studying the mathematical foundations of computing with the essential techniques and tools to mathematically analyze computational processes and investigate the theoretical limitations of computing. The textbook begins by introducing the mathematization of "mechanical processes" through Universal Recursive Modelling (URM) programs, laying the foundation for fundamental concepts such as primitive recursive functions and predicates, sequence-coding, partial recursive functions and predicates, and loop programs. As the survey progresses, advanced chapters delve into topics such as the Ackerman function, Tarskis theorem on the non-representability of truth, Goedels incompleteness and Rosser's incompleteness theorems, two concise proofs of the incompleteness theorem utilizing Lob's deliverability conditions, Church's thesis, the second recursion theorem, applications, a provably recursive universal function for primitive recursive functions, Oracle computations, various classes of computable functionals, the Arithmetical hierarchy, Turing reducibility and Turing degrees, and the priority method. These chapters offer a thorough exposition of various versions of the first recursive theorem, Blums complexity, Hierarchies of primitive recursive functions, and a machine-independent characterisation of Cobham's feasibly computable functions. By encompassing a wide range of topics, this survey serves as a valuable resource for scholars seeking to deepen their understanding of computability theory and its applications in the fields of computer science, mathematics, and philosophy.
Weight: 1132g
Dimension: 161 x 244 x 47 (mm)
ISBN-13: 9783030832018
Edition number: 1st ed. 2022
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