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1.

図書
図書
1. Computation : computability, similarity, and duality (pbk. ; Wiley : pbk.)
Hong Jia-Wei
出版情報: London : Pitman , New York : J. Wiley, 1986  236 p. ; 25 cm
シリーズ名: Research notes in theoretical computer science
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2.

図書
図書
2. Theory of recursive functions and effective computability
Hartley Rogers, Jr.
出版情報: New York : McGraw-Hill, c1967  xix, 482 p. ; 23 cm
シリーズ名: McGraw-Hill series in higher mathematics
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3.

図書
図書
3. Computability and logic (: U.K. - : U.S., pbk)
Daniel E. Cohen
出版情報: Chichester, West Sussex, England : E. Horwood , New York : Halsted Press [distributor], 1987  243 p. ; 25 cm
シリーズ名: Ellis Horwood series in mathematics and its applications
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4.

図書
図書
4. Enumerability, decidability, computability : an introduction to the theory of recursive functions. 2nd rev. ed
Hans Hermes ; translated by G.T. Hermann and O. Plassmann
出版情報: Berlin ; New York : Springer, 1969  x, 245 p. ; 24 cm
シリーズ名: Die Grundlehren der mathematischen Wissenschaften ; Bd. 127
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5.

図書
図書
5. Computability, an introduction to recursive function theory (: pbk)
Nigel Cutland
出版情報: Cambridge [Eng.] ; New York : Cambridge University Press, 1980  x, 251 p. ; 24 cm
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目次情報: 続きを見る
Preface
Prologue. Prerequisites and notation
Sets / 1：
Functions / 2：
Relations and predicates / 3：
Logical notation / 4：
References / 5：
Computable functions
Algorithms, or effective procedures
The unlimited register machine
URM-computable functions
Decidable predicates and problems
Computability on other domains
Generating computable functions
The basic functions
Joining programs together
Substitution
Recursion
Minimalisation
Other approaches to computability: Church's thesis
Other approaches to computability
Partial recursive functions (Godel-Kleene)
A digression: the primitive recursive functions
Turing-computability
Symbol manipulation systems of Post and Markov
Computability on domains other than N / 6：
Church's thesis / 7：
Numbering computable functions
Numbering programs
Discussion: the diagonal method
The s-m-n theorem
Universal programs
Universal functions and universal programs
Two applications of the universal program
Effective operations on computable functions
Computability of the function [sigma subscript n] / Appendix：
Decidability, undecidability and partial decidability
Undecidable problems in computability
The word problem for groups
Diophantine equations
Sturm's algorithm
Mathematical logic
Partially decidable predicates
Recursive and recursively enumerable sets
Recursive sets
Recursively enumerable sets
Productive and creative sets
Simple sets
Arithmetic and Godel's incompleteness theorem / 8：
Formal arithmetic
Incompleteness
Godel's incompleteness theorem
Undecidability
Reducibility and degrees / 9：
Many-one reducibility
Degrees
m-complete r.e. sets
Relative computability
Turing reducibility and Turing degrees
Effective operations on partial functions / 10：
Recursive operators
The first Recursion theorem
An application to the semantics of programming languages
The second Recursion theorem / 11：
Discussion
Myhill's theorem
Complexity of computation / 12：
Complexity and complexity measures
The Speed-up theorem
Complexity classes
The elementary functions
Further study / 13：
Bibliography
Index of notation
Subject Index
Preface
Prologue. Prerequisites and notation
Sets / 1：
6.

図書
図書
6. Recursively enumerable sets and degrees : a study of computable functions and computably generated sets (: U.S. ; : Germany)
Robert I. Soare
出版情報: Berlin ; Tokyo : Springer-Verlag, c1987  xviii, 437 p. ; 25 cm
シリーズ名: Perspectives in mathematical logic
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7.

図書
図書
7. Computability (: us ; : gw)
Klaus Weihrauch
出版情報: Berlin ; Tokyo : Springer-Verlag, c1987  x, 517 p. ; 25 cm
シリーズ名: EATCS monographs on theoretical computer science ; v. 9
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8.

図書
図書
8. Computability theory, semantics, and logic programming
Melvin Fitting
出版情報: New York : Oxford University Press , Oxford : Clarendon Press, 1987  xi, 198 p. ; 25 cm
シリーズ名: Oxford logic guides ; 13
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目次情報: 続きを見る
A String Manipulation Language / Part 1：
Language Background / 1：
Informalities / 2：
Syntax / 3：
Operational Semantics / 4：
Expanding a Work Space / 5：
Program Verification / 6：
Denotational Semantics / 7：
Background and References / 8：
The Family of EFS Languages / Part 2：
EFS Languages
Numbers
Binary Trees
Sets
A Relational Data Base
Logical Notation
Bounded Quantification
Models and Program Correctness
Procedure Completeness / 9：
Operators / 10：
Introduction
Monotone Operators
The Least Fixed Point Theorem
Approximating to a Least Fixed Point
More on Monotone Operators
Procedures That Accept Input
Procedures as Operators
More on Models
The First Recursion Theorem
A Second Proof / 11：
Applications / 12：
A Normal Form Theorem / 13：
Implementing Data Structures / 14：
Codings
Implementations
Conservative Implementations
Different Sized Alphabets
Numbers and Words
Trees and Words
Sets and Words
Implementability
The Church-Turing Thesis / Part 5：
Register Machines
Computations
Computation States
Translating Register Machines into EFS(str(L))
An Imperative Language IMP
Implementing IMP
Enhancing and Restricting IMP
A Logic-Based Language LOG(L)
EFS and LOG
LOG and IMP
Programming Language Equivalences
Efficiency
Programs as Data / 15：
The Alphabet
Elementary Syntax
Procedure Execution
Introducing Constants
Indexes
Some Positive Results
Complements
The Halting Problem
The Universal Quantifier
The Second Recursion Theorem
Rice's Theorem
A String Manipulation Language / Part 1：
Language Background / 1：
Informalities / 2：
9.

図書
図書
9. The undecidable : basic papers on undecidable propositions, unsolvable problems and computable functions
edited by Martin Davis
出版情報: Hewlett, N.Y. : Raven Press, c1965  440 p. ; 25 cm
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On Formally Undecidable Propositions of the Principia Mathematica and Related Systems. I / Kurt Godel
On Undecidable Propositions of Formal Mathematical Systems
On Intuitionistic Arithmetic and Number Theory
On the Length of Proofs
Remarks Before the Princeton Bicentennial Conference on Problems in Mathematics
An Unsolvable Problem of Elementary Number Theory / Alonzo Church
A Note on the Entscheidungsproblem
On Computable Numbers, with an Application to the Entscheidungsproblem / Alan M. Turing
Systems of Logic Based on Ordinals
An Informal Exposition of Proofs of Godel's Theorem and Church's Theorem / J. B. Rosser
Extensions of Some Theorems of Godel and Church
General Recursive Functions of Natural Numbers / Stephen C. Kleene
Recursive Predicates and Quantifiers
Finite Combinatory Processes. Formulation I / Emil Post
Recursive Unsolvability of a Problem of Thue
Recursively Enumerable Sets of Positive Integers and Their Decision Problems
Absolutely Unsolvable Problems and Relatively Undecidable Propositions- Account of an Anticipation
Index
On Formally Undecidable Propositions of the Principia Mathematica and Related Systems. I / Kurt Godel
On Undecidable Propositions of Formal Mathematical Systems
On Intuitionistic Arithmetic and Number Theory
10.

図書
図書
10. Computability & unsolvability
Martin Davis
出版情報: New York ; Toronto ; London : McGraw-Hill, 1958  xxv, 210 p. ; 24 cm
シリーズ名: McGraw-Hill series in information processing and computers
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