Information and randomness: an algorithmic perspective
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | German |
| Veröffentlicht: |
Berlin
Springer
2002
|
| Ausgabe: | 2. ed., rev. and extended |
| Schriftenreihe: | Texts in theoretical computer science
|
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | Literaturverz. S. 419 - 453 |
| Beschreibung: | XX, 467 S. |
| ISBN: | 3540434666 |
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Datensatz im Suchindex
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| adam_text |
CRISTIAN S. CALUDE INFORMATION AND RANDOMNESS AN ALGORITHMIC PERSPECTIVE
SECOND EDITION, REVISED AND EXTENDED FOREWORDS BY GREGORY J. CHAITIN AND
ARTO SALOMAA SPRINGER CONTENTS 1 MATHEMATICAL BACKGROUND 1 1.1
PREREQUISITES 1 1.2 COMPUTABILITY THEORY 4 1.3 TOPOLOGY 6 1.4
PROBABILITY THEORY . 8 1.5 EXERCISES AND PROBLEMS 19 2 NOISELESS CODING
21 2.1 PREFIX-FREE SETS 21 2.2 INSTANTANEOUS CODING 24 2.3' EXERCISES
AND PROBLEMS 30 2.4 HISTORY OF RESULTS 32 3 PROGRAM-SIZE 33 3.1 AN
EXAMPLE 33 3.2 COMPUTERS AND COMPLEXITIES 34 3.3 ALGORITHMIC PROPERTIES
OF COMPLEXITIES 43 3.4 QUANTITATIVE ESTIMATES 45 3.5 HALTING
PROBABILITIES 47 3.6 EXERCISES AND PROBLEMS 49 3.7 HISTORY OF RESULTS /
52 XVIII CONTENTS 4 COMPUTABLY ENUMERABLE INSTANTANEOUS CODES 53 4.1 THE
KRAFT-CHAITIN THEOREM 53 4.2 RELATIVIZED COMPLEXITIES AND PROBABILITIES
60 4.3 SPEED-UP THEOREM 70 4.4 ALGORITHMIC CODING THEOREM . . ~ . 74 4.5
BINARY VS NON-BINARY CODING (1) 85 4.6 EXERCISES AND PROBLEMS 89 4.7
HISTORY OF RESULTS 91 5 RANDOM STRINGS 95 5.1 AN EMPIRICAL ANALYSIS 95
5.2 CHAITIN'S DEFINITION OF RANDOM STRINGS 102 5.3 RELATING COMPLEXITIES
K AND H 107 5.4 A STATISTICAL ANALYSIS 109 5.5 A COMPUTATIONAL ANALYSIS
119 5.6 BOREL NORMALITY 123 5.7 EXTENSIONS OF RANDOM STRINGS 131 5.8
BINARY VS NON-BINARY CODING (2) 136 5.9 EXERCISES AND PROBLEMS 140 5.10
HISTORY OF RESULTS 145 6 RANDOM SEQUENCES 147 6.1 FROM RANDOM STRINGS TO
RANDOM SEQUENCES 147 6.2 THE DEFINITION OF RANDOM SEQUENCES 158 6.3
CHARACTERIZATIONS OF RANDOM SEQUENCES 169 6.4 PROPERTIES OF RANDOM
SEQUENCES 184 6.5 THE REDUCIBILITY THEOREM 204 6.6 THE RANDOMNESS
HYPOTHESIS 229 6.7 EXERCISES AND PROBLEMS , 231 CONTENTS XIX 6.8 HISTORY
OF RESULTS 233 7 COMPUTABLY ENUMERABLE RANDOM. REALS 237 7.1 CHAITIN'S
OMEGA NUMBER 237 7.2 IS RANDOMNESS BASE INVARIANT? 240 7.3 MOST REALS
OBEY NO PROBABILITY LAWS 253 7.4 COMPUTABLE AND UNCOMPUTABLE REALS 260
7.5 COMPUTABLY ENUMERABLE REALS, DOMINATION AND DEGREES 271 7.6 A
CHARACTERIZATION OF COMPUTABLY ENUMERABLE RANDOM REALS 294 7.7
DEGREE-THEORETIC PROPERTIES OF COMPUTABLY ENUMERABLE RANDOM REALS 302
7.8 EXERCISES AND PROBLEMS 310 7.9 HISTORY OF RESULTS 313 8 RANDOMNESS
AND INCOMPLETENESS 315 8.1 THE INCOMPLETENESS PHENOMENON 315 8.2
INFORMATION-THEORETIC INCOMPLETENESS (1) 320 8.3 INFORMATION-THEORETIC
INCOMPLETENESS (2) 324 8.4 INFORMATION-THEORETIC INCOMPLETENESS (3) 328
8.5 CODING MATHEMATICAL KNOWLEDGE 332 8.6 FINITELY REFUTABLE
MATHEMATICAL PROBLEMS 335 8.7 COMPUTING 64 BITS OF A COMPUTABLY
ENUMERABLE RANDOM REAL . 343 8.8 TURING'S BAERRIER REVISITED 355 8.9
HISTORY OF RESULTS 358 9 APPLICATIONS 361 9.1 THE INFINITY OF PRIMES 361
9.2 THE UNDECIDABILITY OF THE HALTING PROBLEM 362 XX CONTENTS 9.3
COUNTING AS A SOURCE OF RANDOMNESS 363 9.4 RANDOMNESS AND CHAOS 366 9.5
RANDOMNESS AND CELLULAR AUTOMATA 367 9.6 RANDOM SEQUENCES OF REALS AND
RIEMANN'S ZETA-FUNCTION 383 9.7 PROBABILISTIC ALGORITHMS 389 9.8
STRUCTURAL COMPLEXITY 393 9.9 WHAT IS LIFE? 398 9.10 RANDOMNESS IN
PHYSICS 405 9.11 METAPHYSICAL THEMES 409 10 OPEN PROBLEMS 415
BIBLIOGRAPHY 419 NOTATION INDEX 455 SUBJECT INDEX 457 NAME INDEX 461 |
| adam_txt |
CRISTIAN S. CALUDE INFORMATION AND RANDOMNESS AN ALGORITHMIC PERSPECTIVE
SECOND EDITION, REVISED AND EXTENDED FOREWORDS BY GREGORY J. CHAITIN AND
ARTO SALOMAA SPRINGER CONTENTS 1 MATHEMATICAL BACKGROUND 1 1.1
PREREQUISITES 1 1.2 COMPUTABILITY THEORY 4 1.3 TOPOLOGY 6 1.4
PROBABILITY THEORY . 8 1.5 EXERCISES AND PROBLEMS 19 2 NOISELESS CODING
21 2.1 PREFIX-FREE SETS 21 2.2 INSTANTANEOUS CODING 24 2.3' EXERCISES
AND PROBLEMS 30 2.4 HISTORY OF RESULTS 32 3 PROGRAM-SIZE 33 3.1 AN
EXAMPLE 33 3.2 COMPUTERS AND COMPLEXITIES 34 3.3 ALGORITHMIC PROPERTIES
OF COMPLEXITIES 43 3.4 QUANTITATIVE ESTIMATES 45 3.5 HALTING
PROBABILITIES 47 3.6 EXERCISES AND PROBLEMS 49 3.7 HISTORY OF RESULTS /
52 XVIII CONTENTS 4 COMPUTABLY ENUMERABLE INSTANTANEOUS CODES 53 4.1 THE
KRAFT-CHAITIN THEOREM 53 4.2 RELATIVIZED COMPLEXITIES AND PROBABILITIES
60 4.3 SPEED-UP THEOREM 70 4.4 ALGORITHMIC CODING THEOREM . . ~ . 74 4.5
BINARY VS NON-BINARY CODING (1) 85 4.6 EXERCISES AND PROBLEMS 89 4.7
HISTORY OF RESULTS 91 5 RANDOM STRINGS 95 5.1 AN EMPIRICAL ANALYSIS 95
5.2 CHAITIN'S DEFINITION OF RANDOM STRINGS 102 5.3 RELATING COMPLEXITIES
K AND H 107 5.4 A STATISTICAL ANALYSIS 109 5.5 A COMPUTATIONAL ANALYSIS
119 5.6 BOREL NORMALITY 123 5.7 EXTENSIONS OF RANDOM STRINGS 131 5.8
BINARY VS NON-BINARY CODING (2) 136 5.9 EXERCISES AND PROBLEMS 140 5.10
HISTORY OF RESULTS 145 6 RANDOM SEQUENCES 147 6.1 FROM RANDOM STRINGS TO
RANDOM SEQUENCES 147 6.2 THE DEFINITION OF RANDOM SEQUENCES 158 6.3
CHARACTERIZATIONS OF RANDOM SEQUENCES 169 6.4 PROPERTIES OF RANDOM
SEQUENCES 184 6.5 THE REDUCIBILITY THEOREM 204 6.6 THE RANDOMNESS
HYPOTHESIS 229 6.7 EXERCISES AND PROBLEMS , 231 CONTENTS XIX 6.8 HISTORY
OF RESULTS 233 7 COMPUTABLY ENUMERABLE RANDOM. REALS 237 7.1 CHAITIN'S
OMEGA NUMBER 237 7.2 IS RANDOMNESS BASE INVARIANT? 240 7.3 MOST REALS
OBEY NO PROBABILITY LAWS 253 7.4 COMPUTABLE AND UNCOMPUTABLE REALS 260
7.5 COMPUTABLY ENUMERABLE REALS, DOMINATION AND DEGREES 271 7.6 A
CHARACTERIZATION OF COMPUTABLY ENUMERABLE RANDOM REALS 294 7.7
DEGREE-THEORETIC PROPERTIES OF COMPUTABLY ENUMERABLE RANDOM REALS 302
7.8 EXERCISES AND PROBLEMS 310 7.9 HISTORY OF RESULTS 313 8 RANDOMNESS
AND INCOMPLETENESS 315 8.1 THE INCOMPLETENESS PHENOMENON 315 8.2
INFORMATION-THEORETIC INCOMPLETENESS (1) 320 8.3 INFORMATION-THEORETIC
INCOMPLETENESS (2) 324 8.4 INFORMATION-THEORETIC INCOMPLETENESS (3) 328
8.5 CODING MATHEMATICAL KNOWLEDGE 332 8.6 FINITELY REFUTABLE
MATHEMATICAL PROBLEMS 335 8.7 COMPUTING 64 BITS OF A COMPUTABLY
ENUMERABLE RANDOM REAL . 343 8.8 TURING'S BAERRIER REVISITED 355 8.9
HISTORY OF RESULTS 358 9 APPLICATIONS 361 9.1 THE INFINITY OF PRIMES 361
9.2 THE UNDECIDABILITY OF THE HALTING PROBLEM 362 XX CONTENTS 9.3
COUNTING AS A SOURCE OF RANDOMNESS 363 9.4 RANDOMNESS AND CHAOS 366 9.5
RANDOMNESS AND CELLULAR AUTOMATA 367 9.6 RANDOM SEQUENCES OF REALS AND
RIEMANN'S ZETA-FUNCTION 383 9.7 PROBABILISTIC ALGORITHMS 389 9.8
STRUCTURAL COMPLEXITY 393 9.9 WHAT IS LIFE? 398 9.10 RANDOMNESS IN
PHYSICS 405 9.11 METAPHYSICAL THEMES 409 10 OPEN PROBLEMS 415
BIBLIOGRAPHY 419 NOTATION INDEX 455 SUBJECT INDEX 457 NAME INDEX 461 |
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| dewey-full | 616.9/2 |
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| dewey-sort | 3616.9 12 |
| dewey-tens | 610 - Medicine and health |
| discipline | Informatik Philosophie Medizin |
| discipline_str_mv | Informatik Philosophie Medizin |
| edition | 2. ed., rev. and extended |
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| illustrated | Not Illustrated |
| index_date | 2024-07-02T18:07:49Z |
| indexdate | 2024-08-01T00:27:56Z |
| institution | BVB |
| isbn | 3540434666 |
| language | German |
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| physical | XX, 467 S. |
| publishDate | 2002 |
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| series2 | Texts in theoretical computer science |
| spelling | Calude, Cristian 1952- Verfasser (DE-588)120988259 aut Information and randomness an algorithmic perspective Cristian S. Calude. Forewords by Gregory J. Chaitin and Arto Salomaa 2. ed., rev. and extended Berlin Springer 2002 XX, 467 S. txt rdacontent n rdamedia nc rdacarrier Texts in theoretical computer science Literaturverz. S. 419 - 453 Computational complexity Machine theory Stochastic processes Automatentheorie (DE-588)4003953-5 gnd rswk-swf Informationstheorie (DE-588)4026927-9 gnd rswk-swf Stochastischer Prozess (DE-588)4057630-9 gnd rswk-swf Automatentheorie (DE-588)4003953-5 s Stochastischer Prozess (DE-588)4057630-9 s DE-604 Informationstheorie (DE-588)4026927-9 s 1\p DE-604 HEBIS Datenaustausch Darmstadt application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=015741064&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Calude, Cristian 1952- Information and randomness an algorithmic perspective Computational complexity Machine theory Stochastic processes Automatentheorie (DE-588)4003953-5 gnd Informationstheorie (DE-588)4026927-9 gnd Stochastischer Prozess (DE-588)4057630-9 gnd |
| subject_GND | (DE-588)4003953-5 (DE-588)4026927-9 (DE-588)4057630-9 |
| title | Information and randomness an algorithmic perspective |
| title_auth | Information and randomness an algorithmic perspective |
| title_exact_search | Information and randomness an algorithmic perspective |
| title_exact_search_txtP | Information and randomness an algorithmic perspective |
| title_full | Information and randomness an algorithmic perspective Cristian S. Calude. Forewords by Gregory J. Chaitin and Arto Salomaa |
| title_fullStr | Information and randomness an algorithmic perspective Cristian S. Calude. Forewords by Gregory J. Chaitin and Arto Salomaa |
| title_full_unstemmed | Information and randomness an algorithmic perspective Cristian S. Calude. Forewords by Gregory J. Chaitin and Arto Salomaa |
| title_short | Information and randomness |
| title_sort | information and randomness an algorithmic perspective |
| title_sub | an algorithmic perspective |
| topic | Computational complexity Machine theory Stochastic processes Automatentheorie (DE-588)4003953-5 gnd Informationstheorie (DE-588)4026927-9 gnd Stochastischer Prozess (DE-588)4057630-9 gnd |
| topic_facet | Computational complexity Machine theory Stochastic processes Automatentheorie Informationstheorie Stochastischer Prozess |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=015741064&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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