Computability (Record no. 178318)

MARC details
000 -LEADER
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001 - CONTROL NUMBER
control field 978-3-030-83202-5
003 - CONTROL NUMBER IDENTIFIER
control field DE-He213
005 - DATE AND TIME OF LATEST TRANSACTION
control field 20240423125455.0
007 - PHYSICAL DESCRIPTION FIXED FIELD--GENERAL INFORMATION
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020 ## - INTERNATIONAL STANDARD BOOK NUMBER
International Standard Book Number 9783030832025
-- 978-3-030-83202-5
024 7# - OTHER STANDARD IDENTIFIER
Standard number or code 10.1007/978-3-030-83202-5
Source of number or code doi
050 #4 - LIBRARY OF CONGRESS CALL NUMBER
Classification number QA75.5-76.95
072 #7 - SUBJECT CATEGORY CODE
Subject category code UYA
Source bicssc
072 #7 - SUBJECT CATEGORY CODE
Subject category code COM014000
Source bisacsh
072 #7 - SUBJECT CATEGORY CODE
Subject category code UYA
Source thema
082 04 - DEWEY DECIMAL CLASSIFICATION NUMBER
Classification number 004.0151
Edition number 23
100 1# - MAIN ENTRY--PERSONAL NAME
Personal name Tourlakis, George.
Relator term author.
Relator code aut
-- http://id.loc.gov/vocabulary/relators/aut
245 10 - TITLE STATEMENT
Title Computability
Medium [electronic resource] /
Statement of responsibility, etc by George Tourlakis.
250 ## - EDITION STATEMENT
Edition statement 1st ed. 2022.
264 #1 -
-- Cham :
-- Springer International Publishing :
-- Imprint: Springer,
-- 2022.
300 ## - PHYSICAL DESCRIPTION
Extent XXVII, 637 p. 12 illus., 10 illus. in color.
Other physical details online resource.
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-- computer
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-- rdamedia
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-- online resource
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-- text file
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505 0# - FORMATTED CONTENTS NOTE
Formatted contents note Mathematical Background; a Review -- A Theory of Computability -- Primitive Recursive Functions -- Loop Programs.-The Ackermann Function -- (Un)Computability via Church's Thesis -- Semi-Recursiveness -- Yet another number-theoretic characterisation of P -- Godel's Incompleteness Theorem via the Halting Problem -- The Recursion Theorem -- A Universal (non-PR) Function for PR -- Enumerations of Recursive and Semi-Recursive Sets -- Creative and Productive Sets Completeness -- Relativised Computability -- POSSIBILITY: Complexity of P Functions -- Complexity of PR Functions -- Turing Machines and NP-Completeness.
520 ## - SUMMARY, ETC.
Summary, etc 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. Features: Extensive and mathematically complete coverage of the limitations of logic, including Gödel’s incompleteness theorems (first and second), Rosser’s version of the first incompleteness theorem, and Tarski’s non expressibility of “truth” Inability of computability to detect formal theorems effectively, using Church’s proof of the unsolvability of Hilbert’s Entscheidungsproblem Arithmetisation-free proof of the pillars of computability: Kleene’s s-m-n, universal function and normal form theorems — using “Church’s thesis” and a simulation of the URM (“register machine”) by a simultaneous recursion. These three pivotal results lead to the deeper results of the theory Extensive coverage of the advanced topic of computation with “oracles" including an exposition of the search computability theory of Moschovakis, the first recursion theorem, Turing reducibility and Turing degrees and an application of the Sacks priority method of “preserving agreements”, and the arithmetical hierarchy including Post’s theorem Cobham’s mathematical characterisation of the concept deterministic polynomial time computable function is fully proved A complete proof of Blum’s speed-up theorem.
650 #0 - SUBJECT ADDED ENTRY--TOPICAL TERM
Topical term or geographic name as entry element Computer science.
650 #0 - SUBJECT ADDED ENTRY--TOPICAL TERM
Topical term or geographic name as entry element Computable functions.
650 #0 - SUBJECT ADDED ENTRY--TOPICAL TERM
Topical term or geographic name as entry element Recursion theory.
650 #0 - SUBJECT ADDED ENTRY--TOPICAL TERM
Topical term or geographic name as entry element Computational complexity.
650 #0 - SUBJECT ADDED ENTRY--TOPICAL TERM
Topical term or geographic name as entry element Technology
General subdivision Philosophy.
650 14 - SUBJECT ADDED ENTRY--TOPICAL TERM
Topical term or geographic name as entry element Theory of Computation.
650 24 - SUBJECT ADDED ENTRY--TOPICAL TERM
Topical term or geographic name as entry element Computability and Recursion Theory.
650 24 - SUBJECT ADDED ENTRY--TOPICAL TERM
Topical term or geographic name as entry element Computational Complexity.
650 24 - SUBJECT ADDED ENTRY--TOPICAL TERM
Topical term or geographic name as entry element Models of Computation.
650 24 - SUBJECT ADDED ENTRY--TOPICAL TERM
Topical term or geographic name as entry element Philosophy of Technology.
710 2# - ADDED ENTRY--CORPORATE NAME
Corporate name or jurisdiction name as entry element SpringerLink (Online service)
773 0# - HOST ITEM ENTRY
Title Springer Nature eBook
776 08 - ADDITIONAL PHYSICAL FORM ENTRY
Display text Printed edition:
International Standard Book Number 9783030832018
776 08 - ADDITIONAL PHYSICAL FORM ENTRY
Display text Printed edition:
International Standard Book Number 9783030832032
776 08 - ADDITIONAL PHYSICAL FORM ENTRY
Display text Printed edition:
International Standard Book Number 9783030832049
856 40 - ELECTRONIC LOCATION AND ACCESS
Uniform Resource Identifier <a href="https://doi.org/10.1007/978-3-030-83202-5">https://doi.org/10.1007/978-3-030-83202-5</a>
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Koha item type eBooks-CSE-Springer

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