Computable functions:
Gespeichert in:
| Hauptverfasser: | , |
|---|---|
| Format: | Buch |
| Sprache: | English Russian |
| Veröffentlicht: |
Providence, R.I.
American Mathematical Society
2003
|
| Schriftenreihe: | Student mathematical library
19 |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | Includes bibliographical references (p. 159-160) and index |
| Beschreibung: | viii, 166 p. ill. : 21 cm |
| ISBN: | 0821827324 |
Internformat
MARC
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| 100 | 1 | |a Šen, Aleksandr Ch. |d 1958- |e Verfasser |0 (DE-588)130558648 |4 aut | |
| 240 | 1 | 0 | |a Vyčislimye funkcii |
| 245 | 1 | 0 | |a Computable functions |c A. Shen, N.K. Vereshchagin ; translated by V.N. Dubrovskii |
| 264 | 1 | |a Providence, R.I. |b American Mathematical Society |c 2003 | |
| 300 | |a viii, 166 p. |b ill. : 21 cm | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 1 | |a Student mathematical library |v 19 | |
| 500 | |a Includes bibliographical references (p. 159-160) and index | ||
| 650 | 4 | |a Fonctions calculables | |
| 650 | 4 | |a Computable functions | |
| 650 | 0 | 7 | |a Berechenbare Funktion |0 (DE-588)4135762-0 |2 gnd |9 rswk-swf |
| 689 | 0 | 0 | |a Berechenbare Funktion |0 (DE-588)4135762-0 |D s |
| 689 | 0 | |5 DE-604 | |
| 700 | 1 | |a Vereščagin, Nikolaj K. |d 1958- |e Verfasser |0 (DE-588)130556548 |4 aut | |
| 830 | 0 | |a Student mathematical library |v 19 |w (DE-604)BV013184751 |9 19 | |
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Datensatz im Suchindex
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| adam_text |
Contents
Preface vii
Chapter 1. Computable Functions, Decidable and Enumerable
Sets 1
§1. Computable functions 1
§2. Decidable sets 3
§3. Enumerable sets 4
§4. Enumerable and decidable sets 7
§5. Enumerability and computability 8
Chapter 2. Universal Functions and Undecidability 11
§1. Universal functions 11
§2. The diagonal construction 13
§3. Enumerable undecidable set 14
§4. Enumerable inseparable sets 16
§5. Simple sets: The Post construction 17
Chapter 3. Numberings and Operations 19
§1. Godel universal functions 19
§2. Computable sequences of computable functions 23
§3. Godel universal sets 24
iii
iv Contents
Chapter 4. Properties of Gödel Numberings 27
§1. Sets of numbers 27
§2. New numbers of old functions 31
§3. Isomorphism of Godel numberings 34
§4. Enumerable properties of functions 36
Chapter 5. Fixed Point Theorem 41
§1. Fixed point and equivalence relations 41
§2. A program that prints its text 44
§3. System trick: Another proof 46
§4. Several remarks 49
Chapter 6. m Reducibility and Properties of Enumerable Sets 55
§1. m reducibility 55
§2. m complete sets 57
§3. m completeness and effective nonenumerability 58
§4. Isomorphism of m complete sets 62
§5. Productive sets 64
§6. Pairs of inseparable sets 67
Chapter 7. Oracle Computations 71
§1. Oracle machines 71
§2. Relative computability: Equivalent description 74
§3. Relativization 76
§4. O' computations 79
§5. Incomparable sets 82
§6. Friedberg Muchnik Theorem: The general scheme of
construction 85
§7. Friedberg Muchnik Theorem: Winning conditions 87
§8. Friedberg Muchnik Theorem: The priority method 89
Chapter 8. Arithmetical Hierarchy 93
§1. Classes En and IIn 93
§2. Universal sets in En and IIn 96
§3. The jump operation 98
Contents v
§4. Classification of sets in the hierarchy 103
Chapter 9. Turing Machines 107
§1. Simple computational models:
What do we need them for? 107
§2. Turing machines: The definition 108
§3. Turing machines: Discussion 110
§4. The word problem 113
§5. Simulation of Turing machines 114
§6. Thue systems 118
§7. Semigroups, generators, and relations 120
Chapter 10. Arithmeticity of Computable Functions 123
§1. Programs with a finite number of variables 123
§2. Turing machines and programs 126
§3. Computable functions are arithmetical 128
§4. Tarski and Godel's Theorems 132
§5. Direct proof of Tarski and Godel's Theorems 134
§6. Arithmetical hierarchy and the number of quantifier
alternations 136
Chapter 11. Recursive Functions 139
§1. Primitive recursive functions 139
§2. Examples of primitive recursive functions 140
§3. Primitive recursive sets 141
§4. Other forms of recursion 143
§5. Turing machines and primitive recursive functions 146
§6. Partial recursive functions 148
§7. Oracle computability 152
§8. Estimates of growth rate. Ackermann's function 154
Bibliography 159
Glossary 161
Index 163 |
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| id | DE-604.BV014831893 |
| illustrated | Illustrated |
| indexdate | 2024-08-01T00:27:50Z |
| institution | BVB |
| isbn | 0821827324 |
| language | English Russian |
| lccn | 2002038567 |
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| owner_facet | DE-20 |
| physical | viii, 166 p. ill. : 21 cm |
| publishDate | 2003 |
| publishDateSearch | 2003 |
| publishDateSort | 2003 |
| publisher | American Mathematical Society |
| record_format | marc |
| series | Student mathematical library |
| series2 | Student mathematical library |
| spelling | Šen, Aleksandr Ch. 1958- Verfasser (DE-588)130558648 aut Vyčislimye funkcii Computable functions A. Shen, N.K. Vereshchagin ; translated by V.N. Dubrovskii Providence, R.I. American Mathematical Society 2003 viii, 166 p. ill. : 21 cm txt rdacontent n rdamedia nc rdacarrier Student mathematical library 19 Includes bibliographical references (p. 159-160) and index Fonctions calculables Computable functions Berechenbare Funktion (DE-588)4135762-0 gnd rswk-swf Berechenbare Funktion (DE-588)4135762-0 s DE-604 Vereščagin, Nikolaj K. 1958- Verfasser (DE-588)130556548 aut Student mathematical library 19 (DE-604)BV013184751 19 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=010036360&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Šen, Aleksandr Ch. 1958- Vereščagin, Nikolaj K. 1958- Computable functions Student mathematical library Fonctions calculables Computable functions Berechenbare Funktion (DE-588)4135762-0 gnd |
| subject_GND | (DE-588)4135762-0 |
| title | Computable functions |
| title_alt | Vyčislimye funkcii |
| title_auth | Computable functions |
| title_exact_search | Computable functions |
| title_full | Computable functions A. Shen, N.K. Vereshchagin ; translated by V.N. Dubrovskii |
| title_fullStr | Computable functions A. Shen, N.K. Vereshchagin ; translated by V.N. Dubrovskii |
| title_full_unstemmed | Computable functions A. Shen, N.K. Vereshchagin ; translated by V.N. Dubrovskii |
| title_short | Computable functions |
| title_sort | computable functions |
| topic | Fonctions calculables Computable functions Berechenbare Funktion (DE-588)4135762-0 gnd |
| topic_facet | Fonctions calculables Computable functions Berechenbare Funktion |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=010036360&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV013184751 |
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