An introduction to Kolmogorov complexity and its applications:
Gespeichert in:
| Hauptverfasser: | , |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
New York u.a.
Springer
1993
|
| Schriftenreihe: | Texts and monographs in computer science
|
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | XX, 546 S. graph. Darst. |
| ISBN: | 0387940537 3540940537 |
Internformat
MARC
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| 100 | 1 | |a Li, Ming |e Verfasser |4 aut | |
| 245 | 1 | 0 | |a An introduction to Kolmogorov complexity and its applications |c Ming Li ; Paul Vitanyi |
| 264 | 1 | |a New York u.a. |b Springer |c 1993 | |
| 300 | |a XX, 546 S. |b graph. Darst. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 0 | |a Texts and monographs in computer science | |
| 650 | 0 | 7 | |a Kolmogorov-Komplexität |0 (DE-588)4164697-6 |2 gnd |9 rswk-swf |
| 689 | 0 | 0 | |a Kolmogorov-Komplexität |0 (DE-588)4164697-6 |D s |
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| 700 | 1 | |a Vitányi, Paul |d 1944- |e Verfasser |0 (DE-588)1201042623 |4 aut | |
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| 943 | 1 | |a oai:aleph.bib-bvb.de:BVB01-005854608 | |
Datensatz im Suchindex
| _version_ | 1807321322693328896 |
|---|---|
| adam_text |
CONTENTS
PREFACE
V
HOW
TO
USE
THIS
BOOK
.
VIII
ACKNOWLEDGEMENTS
.
X
OUTLINES
OF
ONE-SEMESTER
COURSES
.
XII
LIST
OF FIGURES
.
XIX
1
PRELIMINARIES
1
1.1
A
BRIEF
INTRODUCTION
.
1
1.2
MATHEMATICAL
PRELIMINARIES
.
6
1.2.1
PREREQUISITES
AND
NOTATION
.
6
1.2.2
NUMBERS
AND
COMBINATORICS
.
7
1.2.3
BINARY
STRINGS
.
11
1.2.4
ASYMPTOTICS
NOTATION
.
14
1.3
BASICS
OF
PROBABILITY
THEORY
.
16
1.3.1
KOLMOGOROV
AXIOMS
.
17
1.3.2
CONDITIONAL
PROBABILITY
.
18
1.3.3
CONTINUOUS
SAMPLE
SPACES
.
19
1.4
BASICS
OF
COMPUTABILITY
THEORY
.
22
1.4.1
EFFECTIVE
ENUMERATIONS
AND
UNIVERSAL
MACHINES
.
26
1.4.2
UNDECIDABILITY
OF
THE
HALTING
PROBLEM
.
32
1.4.3
ENUMERABLE
FUNCTIONS
.
34
1.4.4
FEASIBLE
COMPUTATIONS
.
35
1.5
THE
ROOTS
OF
KOLMOGOROV
COMPLEXITY
.
45
1.5.1
RANDOMNESS
.
46
XVI
CONTENTS
1.5.2
PREDICTION
AND
PROBABILITY
.
55
1.5.3
INFORMATION
THEORY
AND
CODING
.
61
1.5.4
STATE
X
SYMBOL
COMPLEXITY
.
79
1.6
HISTORY
AND
REFERENCES
.
80
2
ALGORITHMIC
COMPLEXITY
87
2.1
THE
INVARIANCE
THEOREM
.
90
2.2
INCOMPRESSIBILITY
.
95
2.3
C
AS
AN
INTEGER
FUNCTION
.
101
2.4
RANDOM
FINITE
SEQUENCES
.
105
2.5
*RANDOM
INFINITE
SEQUENCES
.
112
2.6
STATISTICAL
PROPERTIES
OF
FINITE
SEQUENCES
.
126
2.6.1
STATISTICS
OF
O
'
S
AND
1
'
S
.
127
2.6.2
STATISTICS
OF
BLOCKS
.
130
2.6.3
LENGTH
OF
RUNS
.
132
2.7
ALGORITHMIC
PROPERTIES
OF
C
.
134
2.8
ALGORITHMIC
INFORMATION
THEORY
.
140
2.9
HISTORY
AND
REFERENCES
.
165
3
ALGORITHMIC
PREFIX
COMPLEXITY
169
3.1
THE
INVARIANCE
THEOREM
.
171
3.2
INCOMPRESSIBILITY
.
175
3.3
K
AS
AN
INTEGER
FUNCTION
.
177
3.4
RANDOM
FINITE
SEQUENCES
.
177
3.5
*RANDOM
INFINITE
SEQUENCES
.
180
3.6
ALGORITHMIC
PROPERTIES
OF
K
.
188
3.7
*THE
COMPLEXITY
OF
THE
COMPLEXITY
FUNCTION
.
190
3.8
*SYMMETRY
OF
ALGORITHMIC
INFORMATION
.
194
3.9
HISTORY
AND
REFERENCES
.
209
4
ALGORITHMIC
PROBABILITY
211
4.1
ENUMERABLE
FUNCTIONS
REVISITED
.
212
4.2
A
NONCLASSICAL
APPROACH
TO
MEASURES
.
214
4.3
DISCRETE
SAMPLE
SPACE
.
216
4.3.1
UNIVERSAL
ENUMERABLE
SEMIMEASURE
.
217
4.3.2
A
PRIORI
PROBABILITY
.
221
4.3.3
ALGORITHMIC
PROBABILITY
.
223
4.3.4
THE
CODING
THEOREM
.
223
4.3.5
RANDOMNESS
BY
SUM
TESTS
.
228
4.3.6
RANDOMNESS
BY
PAYOFF
FUNCTIONS
.
232
4.4
CONTINUOUS
SAMPLE
SPACE
.
234
4.4.1
UNIVERSAL
ENUMERABLE
SEMIMEASURE
.
234
4.4.2
A
PRIORI
PROBABILITY
.
238
4.4.3
*SOLOMONOFF
NORMALIZATION
.
242
4.4.4
*MONOTONE
COMPLEXITY
AND
A
CODING
THEOREM
.
.
243
CONTENTS
XVII
4.4.5
*RELATION
BETWEEN
COMPLEXITIES
.
246
4.4.6
*RANDOMNESS
BY
INTEGRAL
TESTS
.
247
4.4.7
*RANDOMNESS
BY
MARTINGALE
TESTS
.
254
4.4.8
*RANDOMNESS
BY
MARTINGALES
.
256
4.4.9
*RELATIONS
BETWEEN
TESTS
.
258
4.5
HISTORY
AND
REFERENCES
.
268
5
INDUCTIVE
REASONING
275
5.1
INTRODUCTION
.
275
5.2
BAYESIAN
REASONING
.
279
5.3
SOLOMONOFF
'
S
INDUCTION
THEORY
.
282
5.3.1
FORMAL
ANALYSIS
.
284
5.3.2
APPLICATION
TO
INDUCTION
.
290
5.4
RECURSION
THEORY
INDUCTION
.
291
5.4.1
INFERENCE
OF
HYPOTHESES
.
291
5.4.2
PREDICTION
.
292
5.4.3
MISTAKE
BOUNDS
.
293
5.4.4
CERTIFICATION
.
294
5.5
PAC-LEARNING
.
295
5.5.1
DEFINITIONS
.
296
5.5.2
OCCAM
'
S
RAZOR
FORMALIZED
.
296
5.6
SIMPLE
PAC-LEARNING
.
300
5.6.1
DISCRETE
SAMPLE
SPACE
.
301
5.6.2
CONTINUOUS
SAMPLE
SPACE
.
305
5.7
MINIMUM
DESCRIPTION
LENGTH
.
308
5.8
HISTORY
AND
REFERENCES
.
318
6
THE
INCOMPRESSIBILITY
METHOD
323
6.1
TWO
EXAMPLES
.
324
6.2
COMBINATORICS
.
328
6.3
AVERAGE
CASE
COMPLEXITY
OF
ALGORITHMS
.
334
6.3.1
HEAPSORT
.
334
6.3.2
LONGEST
COMMON
SUBSEQUENCE
.
338
6.3.3
M-AVERAGE
CASE
COMPLEXITY
.
340
6.4
LANGUAGES
.
344
6.4.1
FORMAL
LANGUAGE
THEORY
.
344
6.4.2
ON-LINE
CFL
RECOGNITION
.
349
6.4.3
MULTIHEAD
AUTOMATA
.
351
6.5
MACHINES
.
356
6.5.1
*TURING
MACHINE
TIME
COMPLEXITY
.
356
6.5.2
PARALLEL
COMPUTATION
.
362
6.6
HISTORY
AND
REFERENCES
.
370
XVIII
CONTENTS
7
RESOURCE-BOUNDED
COMPLEXITY
377
7.1
MATHEMATICAL
THEORY
.
378
7.1.1
COMPUTABLE
MAJORANTS
.
381
7.1.2
RESOURCE-BOUNDED
HIERARCHIES
.
386
7.2
LANGUAGE
COMPRESSION
.
392
7.2.1
WITH
AN
ORACLE
.
393
7.2.2
WITHOUT
AN
ORACLE
.
396
7.2.3
RANKING
.
399
7.3
COMPUTATIONAL
COMPLEXITY
.
401
7.3.1
CONSTRUCTING
ORACLES
.
402
7.3.2
P-PRINTABILITY
.
405
7.3.3
INSTANCE
COMPLEXITY
.
406
7.4
KT
COMPLEXITY
.
410
7.4.1
UNIVERSAL
OPTIMAL
SEARCH
.
411
7.4.2
POTENTIAL
.
413
7.5
LOGICAL
DEPTH
.
421
7.6
HISTORY
AND
REFERENCES
.
428
8
PHYSICS
AND
COMPUTATION
433
8.1
REVERSIBLE
COMPUTATION
.
434
8.1.1
ENERGY
DISSIPATION
.
434
8.1.2
REVERSIBLE
LOGIC
CIRCUITS
.
435
8.1.3
A
BALLISTIC
COMPUTER
.
436
8.1.4
REVERSIBLE
TURING
MACHINES
.
439
8.2
INFORMATION
DISTANCE
.
441
8.2.1
MAX
DISTANCE
.
442
8.2.2
PICTURE
DISTANCE
.
446
8.2.3
REVERSIBLE
DISTANCE
.
448
8.2.4
SUM
DISTANCE
.
450
8.2.5
METRICS
RELATIONS
AND
DIMENSIONAL
PROPERTIES
.
452
8.2.6
THERMODYNAMICS
OF
COMPUTING
.
455
8.3
THERMODYNAMICS
.
458
8.3.1
CLASSICAL
ENTROPY
.
458
8.3.2
STATISTICAL
MECHANICS
AND
BOLTZMANN
ENTROPY
.
461
8.3.3
GIBBS
ENTROPY
.
467
8.4
ENTROPY
REVISITED
.
468
8.4.1
ALGORITHMIC
ENTROPY
.
469
8.4.2
ALGORITHMIC
ENTROPY
AND
RANDOMNESS
TESTS
.
473
8.4.3
ENTROPY
STABILITY
AND
NONDECREASE
.
478
8.5
CHAOS,
BIOLOGY,
AND
ALL
THAT
.
486
8.6
HISTORY
AND
REFERENCES
.
490
BIBLIOGRAPHY
493
INDEX
527 |
| any_adam_object | 1 |
| author | Li, Ming Vitányi, Paul 1944- |
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| author_facet | Li, Ming Vitányi, Paul 1944- |
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| id | DE-604.BV008853598 |
| illustrated | Illustrated |
| indexdate | 2024-08-14T00:38:45Z |
| institution | BVB |
| isbn | 0387940537 3540940537 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-005854608 |
| oclc_num | 246670650 |
| open_access_boolean | |
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| owner_facet | DE-20 DE-91G DE-BY-TUM DE-384 DE-29 DE-29T DE-706 DE-634 DE-83 DE-11 DE-188 |
| physical | XX, 546 S. graph. Darst. |
| publishDate | 1993 |
| publishDateSearch | 1993 |
| publishDateSort | 1993 |
| publisher | Springer |
| record_format | marc |
| series2 | Texts and monographs in computer science |
| spelling | Li, Ming Verfasser aut An introduction to Kolmogorov complexity and its applications Ming Li ; Paul Vitanyi New York u.a. Springer 1993 XX, 546 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Texts and monographs in computer science Kolmogorov-Komplexität (DE-588)4164697-6 gnd rswk-swf Kolmogorov-Komplexität (DE-588)4164697-6 s DE-604 Vitányi, Paul 1944- Verfasser (DE-588)1201042623 aut DNB Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=005854608&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Li, Ming Vitányi, Paul 1944- An introduction to Kolmogorov complexity and its applications Kolmogorov-Komplexität (DE-588)4164697-6 gnd |
| subject_GND | (DE-588)4164697-6 |
| title | An introduction to Kolmogorov complexity and its applications |
| title_auth | An introduction to Kolmogorov complexity and its applications |
| title_exact_search | An introduction to Kolmogorov complexity and its applications |
| title_full | An introduction to Kolmogorov complexity and its applications Ming Li ; Paul Vitanyi |
| title_fullStr | An introduction to Kolmogorov complexity and its applications Ming Li ; Paul Vitanyi |
| title_full_unstemmed | An introduction to Kolmogorov complexity and its applications Ming Li ; Paul Vitanyi |
| title_short | An introduction to Kolmogorov complexity and its applications |
| title_sort | an introduction to kolmogorov complexity and its applications |
| topic | Kolmogorov-Komplexität (DE-588)4164697-6 gnd |
| topic_facet | Kolmogorov-Komplexität |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=005854608&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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