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Computability (1st ed. 2022)
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Computability (1st ed. 2022)
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This survey of computability theory offers the techniques and tools
that computer scientists (as well as mathematicians and
philosophers studying the mathematical foundations of computing)
need to mathematically analyze computational processes and
investigate the theoretical limitations of computing. Beginning
with an introduction to the mathematisation of “mechanical
process” using URM programs, this textbook explains basic theory
such as primitive recursive functions and predicates and
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,
Goedel’s incompleteness and Rosser’s incompleteness theorems,
two short proofs of the incompleteness theorem that are 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.
General
Imprint: |
Springer Nature Switzerland AG
|
Country of origin: |
Switzerland |
Release date: |
August 2023 |
Firstpublished: |
2022 |
Authors: |
George Tourlakis
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Dimensions: |
235 x 155mm (L x W) |
Pages: |
637 |
Edition: |
1st ed. 2022 |
ISBN-13: |
978-3-03-083204-9 |
Categories: |
Books
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LSN: |
3-03-083204-X |
Barcode: |
9783030832049 |
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