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Computability (Hardcover, 1st ed. 2022)
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Computability (Hardcover, 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.
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