Turing’s revolution: the impact of his ideas about computability
Gespeichert in:
| Weitere beteiligte Personen: | , |
|---|---|
| Format: | Buch |
| Sprache: | Englisch |
| Veröffentlicht: |
Cham
Birkhäuser
[2015]
|
| Schlagwörter: | |
| Links: | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=028835092&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| Umfang: | xxiv, 329 Seiten Illustrationen, Diagramme (teilweise farbig) 24 cm |
| ISBN: | 9783319221557 |
Internformat
MARC
| LEADER | 00000nam a2200000 c 4500 | ||
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| 003 | DE-604 | ||
| 005 | 20170505 | ||
| 007 | t| | ||
| 008 | 160229s2015 xx a||| |||| 00||| eng d | ||
| 020 | |a 9783319221557 |c hbk |9 978-3-319-22155-7 | ||
| 035 | |a (OCoLC)951018677 | ||
| 035 | |a (DE-599)BVBBV043417004 | ||
| 040 | |a DE-604 |b ger |e rda | ||
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| 084 | |a 03-06 |2 msc | ||
| 245 | 1 | 0 | |a Turing’s revolution |b the impact of his ideas about computability |c Giovanni Sommaruga, Thomas Strahm, editors |
| 264 | 1 | |a Cham |b Birkhäuser |c [2015] | |
| 264 | 4 | |c © 2015 | |
| 300 | |a xxiv, 329 Seiten |b Illustrationen, Diagramme (teilweise farbig) |c 24 cm | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 600 | 1 | 7 | |a Turing, Alan |d 1912-1954 |0 (DE-588)118802976 |2 gnd |9 rswk-swf |
| 650 | 4 | |a Mathematics | |
| 650 | 4 | |a Logic | |
| 650 | 4 | |a History | |
| 650 | 4 | |a Mathematical logic | |
| 650 | 4 | |a Mathematical Logic and Foundations | |
| 650 | 4 | |a History of Mathematical Sciences | |
| 650 | 4 | |a Geschichte | |
| 650 | 4 | |a Mathematik | |
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| 650 | 0 | 7 | |a Mathematik |0 (DE-588)4037944-9 |2 gnd |9 rswk-swf |
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| 689 | 0 | 0 | |a Turing, Alan |d 1912-1954 |0 (DE-588)118802976 |D p |
| 689 | 0 | 1 | |a Mathematik |0 (DE-588)4037944-9 |D s |
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| 700 | 1 | |a Sommaruga, Giovanni |0 (DE-588)1085141594 |4 edt | |
| 700 | 1 | |a Strahm, Thomas |0 (DE-588)1103057448 |4 edt | |
| 776 | 0 | 8 | |i Erscheint auch als |n Online-Ausgabe |z 978-3-319-22156-4 |
| 856 | 4 | 2 | |m Digitalisierung Deutsches Museum |q application/pdf |u http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=028835092&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |3 Inhaltsverzeichnis |
| 943 | 1 | |a oai:aleph.bib-bvb.de:BVB01-028835092 | |
Datensatz im Suchindex
| _version_ | 1819245151264964608 |
|---|---|
| adam_text | CONTENTS
PART
I TURING
AND
THE
HISTORY
OF
COMPUTABILITY
THEORY
CONCEPTUAL
CONFLUENCE
IN 1936:
POST
AND
TURING
............................
3
MARTIN
DAVIS
AND
WILFRIED
SIEG
1
INTRODUCTION
..................................................................
4
2
SUBSTITUTION
PUZZLES:
THE
LINK
..............................................
5
3
EFFECTIVELY
CALCULABLE
FUNCTIONS
............................................
7
4
CANONICAL
SYSTEMS:
POST
.....................................................
10
5
MECHANICAL
PROCEDURES:
TURING
.............................................
14
6
WORD PROBLEMS
...............................................................
17
7
CONCLUDING
REMARKS
.........................................................
22
REFERENCES
.........................................................................
24
ALGORITHMS:
FROM AL-KHWARIZMI TO
TURING
AND
BEYOND
....................
29
WOLFGANG
THOMAS
1
PROLOGUE
......................................................................
29
2
SOME PREHISTORY:
AL-KHWARIZMI
AND
LEIBNIZ
..............................
30
3
TOWARDS HILBERT S
ENTSCHEIDUNGSPROBLEM
..................................
33
4
TURING S BREAKTHROUGH
.......................................................
35
5
MOVES TOWARDS
COMPUTER
SCIENCE
.........................................
36
6
NEW
FACETS
OF
ALGORITHM
.................................................
37
7
ALGORITHMS
AS
MOLECULES
IN LARGE
ORGANISMS
..............................
39
8
RETURNING
TO
LEIBNIZIAN
VISIONS?
...........................................
40
REFERENCES
.........................................................................
41
THE
STORED-PROGRAM
UNIVERSAL
COMPUTER:
DID
ZUSE
ANTICIPATE
TURING
AND VON
NEUMANN?
.........................................
43
B.
JACK
COPELAND
AND
GIOVANNI
SOMMARUGA
1
INTRODUCTION
..................................................................
44
2
ZUSE:
A
BRIEF
BIOGRAPHY
....................................................
49
3
TURING,
VON
NEUMANN,
AND
THE
UNIVERSAL
ELECTRONIC
COMPUTER
...........
58
XIX
XX
CONTENTS
4A
HIERARCHY
OF
PROGRAMMING
PARADIGMS
...................................
75
4.1 PARADIGM
P1..........................................................
78
4.2
PARADIGM
P2
..........................................................
78
4.3
PARADIGM
P3
..........................................................
79
4.4
PARADIGM P4
..........................................................
80
4.5
PARADIGM
P5
..........................................................
81
4.6
PARADIGM
P6
..........................................................
81
5
ZUSE
AND
THE
CONCEPT
OF
THE
UNIVERSAL
MACHINE
...........................
85
6
ZUSE
AND
THE
STORED-PROGRAM
CONCEPT
......................................
89
7 CONCLUDING
REMARKS
.........................................................
95
PART II GENERALIZING
TURING
COMPUTABILITY
THEORY
THESES FOR
COMPUTATION
AND
RECURSION
ON
CONCRETE
AND
ABSTRACT STRUCTURES
.........................................................
105
SOLOMON
FEFERMAN
1
INTRODUCTION
..................................................................
105
2
RECURSION
AND
COMPUTATION
ON
THE
NATURAL
NUMBERS,
AND
THE
CHURCH-TURING
THESIS
...............................................
108
3 COMPUTATION
ON
CONCRETE
STRUCTURES
AND
PROOFS
OF
CT
.................
111
4
PROPOSED
GENERALIZATIONS
OF
THEORIES
OF
COMPUTATION
AND
CT
TO
ABSTRACT
STRUCTURES;
THESES
FOR
ALGORITHMS
.............................
114
5
RECURSION
ON
ABSTRACT
STRUCTURES
...........................................
120
REFERENCES
.........................................................................
124
GENERALIZING
COMPUTABILITY
THEORY
TO
ABSTRACT
ALGEBRAS
..................
127
J. V. TUCKER
AND
J.
I. ZUCKER
1 INTRODUCTION
..................................................................
127
2 ON
GENERALIZING
COMPUTABILITY
THEORY
....................................
129
3
WHILE COMPUTATION
ON
STANDARD
MANY-SORTED
TOTAL ALGEBRAS
............
131
3.1
BASIC CONCEPTS: SIGNATURES
AND
PARTIAL ALGEBRAS
...................
132
3.2
SYNTAX
AND
SEMANTICS
OF
E-TERMS
..................................
134
3.3
ADDING COUNTERS:
N-STANDARD SIGNATURES
AND
ALGEBRAS
...........
134
3.4
ADDING
ARRAYS: ALGEBRAS A*
OF
SIGNATURE E*
.....................
135
4 THE
WHILE PROGRAMMING
LANGUAGE
.........................................
135
4.1
WHILE,
WHILEN
AND
WHILE* COMPUTABILITY
.........................
136
5
REPRESENTATIONS
OF
SEMANTIC FUNCTIONS;
UNIVERSALITY
......................
137
5.1
NUMBERING
OF
SYNTAX
................................................
137
5.2
REPRESENTATION
OF
STATES
.............................................
138
5.3
REPRESENTATION
OF
TERM
EVALUATION; TERM
EVALUATION
PROPERTY
...
138
6
CONCEPTS
OF
SEMICOMPUTABILITY
.............................................
140
6.1
MERGING
TWO PROCEDURES;
CLOSURE
THEOREMS
......................
141
6.2
PROJECTIVE
WHILE
SEMICOMPUTABILITY
AND
COMPUTABILITY
...........
143
6.3
WHILE*
SEMICOMPUTABILITY
..........................................
143
6.4
PROJECTIVE
WHILE* SEMICOMPUTABILITY
...............................
144
6.5
COMPUTATION
TREES;
ENGELER S
LEMMA
..............................
144
CONTENTS
XXI
6.6
PROJECTIVE EQUIVALENCE
THEOREM FOR
WHILE
.......................
145
6.7
SEMICOMPUTABILITY
AND
PROJECTIVE SEMICOMPUTABILITY
ON
RT
..................................................................
146
7
COMPUTATION
ON
TOPOLOGICAL PARTIAL
ALGEBRAS
..............................
148
7.1
ABSTRACT
VERSUS CONCRETE
DATA TYPES
OF
REALS;
CONTINUITY;
PARTIALITY
.................................................
148
7.2
EXAMPLES
OF
NONDETERMINISM
AND
MANY-VALUEDNESS
..............
149
7.3
PARTIAL
ALGEBRA
OF
REALS; COMPLETENESS
FOR
THE
ABSTRACT
MODEL
...
152
8
COMPARING
MODELS
AND
GENERALIZING
THE
CHURCH-TURING
THESIS..........
154
8.1
ABSTRACT
MODELS
OF
COMPUTATION
....................................
154
8.2
GENERALIZING
THE
CHURCH-TURING
THESIS
.............................
155
8.3
CONCLUDING
REMARKS
.................................................
157
REFERENCES
.........................................................................
158
DISCRETE
TRANSFINITE
COMPUTATION
..............................................
161
P.
D.
WELCH
I
INTRODUCTION
..................................................................
161
1.1
COMPUTATION
IN
THE
LIMIT
............................................
163
2
WHAT
ITTM S CAN ACHIEVE?
................................................
166
2.1
COMPARISONS
WITH
KLEENE RECURSION
................................
169
2.2
DEGREE THEORY
AND
COMPLEXITY
OF
ITTM COMPUTATIONS...........
173
2.3
TRUTH
AND
ARITHMETICAL
QUASI-INDUCTIVE
SETS
.......................
174
3
VARIANT
ITTM
MODELS
........................................................
175
3.1
LONGER TAPES
.........................................................
176
4
OTHER
TRANSFINITE
MACHINES
..................................................
178
4.1
INFINITE TIME
REGISTER MACHINES
(ITRM S)
.........................
178
4.2
ORDINAL REGISTER
MACHINES
(ORM S)
................................
180
5
INFINITE
TIME BLUM-SHUB-SMALE
MACHINES
(IBSSM S)
....................
181
6
CONCLUSIONS
..................................................................
183
REFERENCES
.........................................................................
184
SEMANTICS-TO-SYNTAX
ANALYSES
OF
ALGORITHMS
.................................
187
YURI
GUREVICH
I
INTRODUCTION
..................................................................
188
1.1
TERMINOLOGY
..........................................................
188
1.2
WHAT S
IN
THE
PAPER?
.................................................
1
90
2
TURING
.........................................................................
192
2.1
TURING S SPECIES
OF
ALGORITHMS
......................................
192
2.2
TURING S
FULCRUM
.....................................................
194
2.3
ON
TURING S RESULTS
AND
ARGUMENTATION
............................
194
2.4
TWO
CRITICAL
QUOTES
..................................................
1 95
3
KOLMOGOROV
..................................................................
1 96
3.1
KOLMOGOROV S SPECIES
OF
ALGORITHMS
...............................
196
3.2
KOLMOGOROV S FULCRUM
..............................................
196
XXII
CONTENTS
4
GANDY
.........................................................................
197
4.1
GANDY S
SPECIES
OF
ALGORITHMS
......................................
197
4.2
GANDY S FULCRUM
.....................................................
199
4.3
COMMENTS
............................................................
1 99
5
SEQUENTIAL
ALGORITHMS
.......................................................
200
5.1
MOTIVATION
............................................................
200
5.2
THE
SPECIES
...........................................................
201
5.3 THE
FULCRUM
..........................................................
203
6 FINAL REMARKS
................................................................
204
REFERENCES
.........................................................................
205
THE
INFORMATION
CONTENT
OF
TYPICAL
REALS
....................................
207
GEORGE
BARMPALIAS
AND
ANDY LEWIS-PYE
I
INTRODUCTION
..................................................................
207
1.1 THE
ALGORITHMIC
VIEW
OF
THE
CONTINUUM
...........................
208
1.2
PROPERTIES
OF
DEGREES
................................................
209
1.3
A HISTORY
OF
MEASURE
AND
CATEGORY
ARGUMENTS
IN
THE
TURING
DEGREES
................................................
210
1.4
OVERVIEW
..............................................................
212
2 TYPICAL
DEGREES
AND
CALIBRATION
OF
TYPICALITY
.............................
213
2.1 LARGE
SETS
AND
TYPICAL
REALS
........................................
213
2.2 PROPERTIES
OF
DEGREES
AND
DEFINABILITY
..............................
215
2.3
VERY
BASIC
QUESTIONS
REMAIN
OPEN
.................................
216
3
PROPERTIES
OF
THE
TYPICAL
DEGREES
AND
THEIR
PREDECESSORS
.................
217
3.1
SOME
PROPERTIES
OF
THE
TYPICAL
DEGREES
............................
217
3.2 PROPERTIES
OF
TYPICAL
DEGREES
ARE
INHERITED
BY
THE
NON-ZERO
DEGREES
THEY
COMPUTE
...........................
219
4
GENERICITY
AND
RANDOMNESS
.................................................
221
REFERENCES
.........................................................................
223
PROOF
THEORETIC
ANALYSIS
BY
ITERATED
REFLECTION
..............................
225
L. D.
BEKLEMISHEV
1 PRELIMINARY
NOTES
............................................................
226
2 INTRODUCTION
..................................................................
229
3
CONSTRUCTING
ITERATED
REFLECTION
PRINCIPLES
.................................
235
4
ITERATED
II2-REFLECTION
AND
THE
FAST
GROWING
HIERARCHY
...................
241
5
UNIFORM
REFLECTION
IS NOT
MUCH
STRONGER
THAN LOCAL
REFLECTION
........
244
6 EXTENDING
CONSERVATION
RESULTS
TO
ITERATED
REFLECTION
PRINCIPLES
........
249
7
SCHMERL S
FORMULA
...........................................................
253
8
ORDINAL
ANALYSIS
OF
FRAGMENTS
..............................................
255
9
CONCLUSION
AND
FURTHER
WORK
...............................................
259
APPENDIX
1
.........................................................................
260
APPENDIX
2
.........................................................................
262
APPENDIX
3
.........................................................................
265
REFERENCES
.........................................................................
269
CONTENTS
XXIII
PART
III
PHILOSOPHICAL
REFLECTIONS
ALAN
LURING
AND
THE
FOUNDATION
OF
COMPUTER
SCIENCE
......................
273
JURAJ
HROMKOVIC
1
WHAT
IS MATHEMATICS?
OR
THE DREAM
OF
LEIBNIZ
........................
273
2
IS
MATHEMATICS PERFECT?
OR
THE DREAM
OF
HILBERT
.......................
275
3
THE
INCOMPLETENESS THEOREM
OF
GOEDEL
AS
THE
END
OF
THE
DREAMS
OF
LEIBNIZ
AND
HILBERT
.......................................
276
4
ALAN
TURING
AND
THE
FOUNDATION
OF
INFORMATICS
............................
278
5
CONCLUSION
...................................................................
281
REFERENCES
.........................................................................
281
PROVING
THINGS ABOUT
THE
INFORMAL
............................................
283
STEWART
SHAPIRO
I
THE
RECEIVED VIEW:
NO PROOF
...............................................
283
2
VAGUENESS:
DOES
CHURCH S THESIS EVEN HAVE
A
TRUTH VALUE?
.............
284
3
THESES
........................................................................
286
4
THE
OPPOSITION: IT IS POSSIBLE
TO
PROVE THESE
THINGS
.....................
286
5
SO
WHAT IS IT
TO
PROVE
SOMETHING?
.........................................
288
6
EPISTEMOLOGY
.................................................................
291
REFERENCES
.........................................................................
295
WHY
TURING S
THESIS IS
NOT
A
THESIS
...........................................
297
ROBERT
IRVING SOARE
I
INTRODUCTION
..................................................................
297
1.1
PRECISION
OF
THOUGHT
AND
TERMINOLOGY
.............................
297
1.2
THE MAIN POINTS
OF
THIS
PAPER
.......................................
298
2
WHAT
IS
A
THESIS?
............................................................
299
3
THE
CONCEPT
OF
EFFECTIVELY
CALCULABLE
.....................................
300
4
TURING S
PAPER
IN 1936
.......................................................
301
4.1
WHAT
IS
A
PROCEDURE?
.................................................
301
4.2
TURING S DEFINITION
OF
EFFECTIVELY CALCULABLE FUNCTIONS
...........
301
4.3
GOEDEL S REACTION
TO
TURING S
PAPER
.................................
302
4.4
CHURCH S
REACTION
TO
TURING S PAPER
................................
302
4.5
KLEENE S
REACTION
TO
TURING S PAPER
................................
302
5
CHURCH
REJECTS POST S WORKING
HYPOTHESIS
..............................
303
6
REMARKS
BY OTHER AUTHORS
..................................................
304
7
GANDY
AND
SIEG: PROVING TURING S THESIS
1.1
..............................
304
7.1
GANDY
.................................................................
304
7.2
SIEG
...................................................................
304
8
FEFERMAN:
CONCRETE
AND
ABSTRACT STRUCTURES
...............................
305
8.1
FEFERMAN S REVIEW
OF
THE
HISTORY
OF
THE
SUBJECT
...................
305
8.2
FEFERMAN
ON
CONCRETE STRUCTURES
....................................
305
8.3
FEFERMAN
ON
KLEENE S
NAMING
OF
CTT
.............................
306
9
GUREVICH:
WHAT
IS
AN
ALGORITHM?
...........................................
306
XXIV
CONTENTS
10
KRIPKE: ON
PROVING TURING S
THESIS
........................................
306
10.1
KRIPKE
ON
COMPUTORABLE FUNCTIONS IN SOARE
.......................
306
10.2 KRIPKE S
SUGGESTED
PROOF
OF
THE
MACHINE THESIS
1.2
..............
307
11 TURING
ON
DEFINITION VERSUS
THEOREM
......................................
307
REFERENCES
.........................................................................
308
INCOMPUTABILITY EMERGENT,
AND
HIGHER
TYPE
COMPUTATION
................
311
S. BARRY COOPER
1 INTRODUCTION
..................................................................
312
2 INCOMPUTABILITY: UNRULY GUEST
AT
THE
COMPUTER S
RECEPTION
.............
314
3 INCOMPUTABILITY, RANDOMNESS
AND
HIGHER TYPE COMPUTATION
.............
316
4 EMBODIMENT
BEYOND
THE
CLASSICAL
MODEL
OF
COMPUTATION
................
320
5
LIVING IN
A
WORLD
OF
HIGHER TYPE
COMPUTATION
............................
323
6 TURING S MATHEMATICAL HOST
.................................................
327
REFERENCES
.........................................................................
329
|
| any_adam_object | 1 |
| author2 | Sommaruga, Giovanni Strahm, Thomas |
| author2_role | edt edt |
| author2_variant | g s gs t s ts |
| author_GND | (DE-588)1085141594 (DE-588)1103057448 |
| author_facet | Sommaruga, Giovanni Strahm, Thomas |
| building | Verbundindex |
| bvnumber | BV043417004 |
| classification_rvk | SF 8465 SR 800 |
| ctrlnum | (OCoLC)951018677 (DE-599)BVBBV043417004 |
| dewey-full | 511.3 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 511 - General principles of mathematics |
| dewey-raw | 511.3 |
| dewey-search | 511.3 |
| dewey-sort | 3511.3 |
| dewey-tens | 510 - Mathematics |
| discipline | Informatik Mathematik |
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| id | DE-604.BV043417004 |
| illustrated | Illustrated |
| indexdate | 2024-12-20T17:35:53Z |
| institution | BVB |
| isbn | 9783319221557 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-028835092 |
| oclc_num | 951018677 |
| open_access_boolean | |
| owner | DE-11 DE-210 DE-83 DE-188 |
| owner_facet | DE-11 DE-210 DE-83 DE-188 |
| physical | xxiv, 329 Seiten Illustrationen, Diagramme (teilweise farbig) 24 cm |
| publishDate | 2015 |
| publishDateSearch | 2015 |
| publishDateSort | 2015 |
| publisher | Birkhäuser |
| record_format | marc |
| spellingShingle | Turing’s revolution the impact of his ideas about computability Turing, Alan 1912-1954 (DE-588)118802976 gnd Mathematics Logic History Mathematical logic Mathematical Logic and Foundations History of Mathematical Sciences Geschichte Mathematik Logik (DE-588)4036202-4 gnd Mathematik (DE-588)4037944-9 gnd Mathematische Logik (DE-588)4037951-6 gnd |
| subject_GND | (DE-588)118802976 (DE-588)4036202-4 (DE-588)4037944-9 (DE-588)4037951-6 |
| title | Turing’s revolution the impact of his ideas about computability |
| title_auth | Turing’s revolution the impact of his ideas about computability |
| title_exact_search | Turing’s revolution the impact of his ideas about computability |
| title_full | Turing’s revolution the impact of his ideas about computability Giovanni Sommaruga, Thomas Strahm, editors |
| title_fullStr | Turing’s revolution the impact of his ideas about computability Giovanni Sommaruga, Thomas Strahm, editors |
| title_full_unstemmed | Turing’s revolution the impact of his ideas about computability Giovanni Sommaruga, Thomas Strahm, editors |
| title_short | Turing’s revolution |
| title_sort | turing s revolution the impact of his ideas about computability |
| title_sub | the impact of his ideas about computability |
| topic | Turing, Alan 1912-1954 (DE-588)118802976 gnd Mathematics Logic History Mathematical logic Mathematical Logic and Foundations History of Mathematical Sciences Geschichte Mathematik Logik (DE-588)4036202-4 gnd Mathematik (DE-588)4037944-9 gnd Mathematische Logik (DE-588)4037951-6 gnd |
| topic_facet | Turing, Alan 1912-1954 Mathematics Logic History Mathematical logic Mathematical Logic and Foundations History of Mathematical Sciences Geschichte Mathematik Logik Mathematische Logik |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=028835092&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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