Computational complexity: a conceptual perspective
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| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Cambridge [u.a.]
Cambridge Univ. Press
2008
|
| Edition: | 1. publ. |
| Subjects: | |
| Online Access: | Contributor biographical information Publisher description Table of contents only Inhaltsverzeichnis |
| Item Description: | Includes bibliographical references and index |
| Physical Description: | XXIV, 606 S. graph. Darst. |
| ISBN: | 9780521884730 |
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MARC
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| 245 | 1 | 0 | |a Computational complexity |b a conceptual perspective |c Oded Goldreich |
| 250 | |a 1. publ. | ||
| 264 | 1 | |a Cambridge [u.a.] |b Cambridge Univ. Press |c 2008 | |
| 300 | |a XXIV, 606 S. |b graph. Darst. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 500 | |a Includes bibliographical references and index | ||
| 650 | 4 | |a Computational complexity | |
| 650 | 4 | |a Turing machines | |
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| 856 | 4 | |u http://www.loc.gov/catdir/enhancements/fy0811/2008006750-t.html |3 Table of contents only | |
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| adam_text | Contents
List of Figures page
xiii
Preface
xv
Organization and Chapter Summaries
xvii
Acknowledgments
xxiii
1
Introduction and Preliminaries
1
1.1
Introduction
1
1.1.1
A Brief Overview of Complexity Theory
2
1.1.2
Characteristics of Complexity Theory
6
1.1.3
Contents of This Book
8
1.4
Approach and Style of This Book
12
1.5
Standard Notations and Other Conventions
16
1.2
Computational Tasks and Models
17
1.2.1
Representation
18
1.2.2
Computational Tasks
18
1.2.3
Uniform Models (Algorithms)
20
1.2.4
Non-uniform Models (Circuits and Advice)
36
1.2.5
Complexity Classes
42
Chapter Notes
43
2
P, NP, and NP-Completeness
44
2.1
The
Ρ
Versus NP Question
46
2.1.1
The Search Version: Finding Versus Checking
47
2.1.2
The Decision Version: Proving Versus Verifying
50
2.1.3
Equivalence of the Two Formulations
54
2.1.4
Two Technical Comments Regarding NP
55
2.1.5
The Traditional Definition of NP
55
2.1.6
In Support of
Ρ
Different from NP
57
2.1.7
Philosophical Meditations
58
2.2
Polynomial-Time Reductions
58
2.2.1
The General Notion of a Reduction
59
2.2.2
Reducing Optimization Problems to Search Problems
61
2.2.3
Self-Reducibility of Search Problems
63
2.2.4
Digest and General Perspective
67
vii
CONTENTS
2.3 NP-Completeness 67
2.3.1
Definitions
68
2.3.2
The Existence of
NP-Complete Problems 69
2.3.3
Some Natural
NP-Complete Problems 71
2.3.4 NP
Sets That Are Neither
in
Ρ
nor NP-Complete
81
2.3.5
Reflections on Complete Problems
85
2.4
Three Relatively Advanced Topics
87
2.4.1
Promise Problems
87
2.4.2
Optimal Search Algorithms for NP
92
2.4.3
The Class coNP and Its Intersection with NP
94
Chapter Notes
97
Exercises
99
3
Variations on
Ρ
and NP
108
3.1
Non-uniform Polynomial Time (P/poly)
108
3.1.1
Boolean Circuits
109
3.1.2
Machines That Take Advice 111
3.2
The Polynomial-Time Hierarchy (PH)
113
3.2.1
Alternation of Quantifiers
114
3.2.2
Non-deterministic Oracle Machines
117
3.2.3
The P/poly Versus NP Question and PH
119
Chapter Notes
121
Exercises
122
4
More Resources, More Power?
127
4.1
Non-uniform Complexity Hierarchies
128
4.2
Time Hierarchies and Gaps
129
4.2.1
Time Hierarchies
129
4.2.2
Time Gaps and Speedup
136
4.3
Space Hierarchies and Gaps
139
Chapter Notes
139
Exercises
140
5
Space Complexity
143
5.1
General Preliminaries and Issues
144
5.1.1
Important Conventions
144
5.1.2
On the Minimal Amount of Useful Computation Space
145
5.1.3
Time Versus Space
146
5.1.4
Circuit Evaluation
153
5.2
Logarithmic Space
153
5.2.1
The Class
L
154
5.2.2
Log-Space Reductions
154
5.2.3
Log-Space Uniformity and Stronger Notions
155
5.2.4
Undirected Connectivity
155
5.3
Non-deterministic Space Complexity
162
5.3.1
Two Models
162
5.3.2
NL and Directed Connectivity
164
5.3.3
A Retrospective Discussion
171
viii
CONTENTS
5.4 PSPACE and Games 172
Chapter
Notes 175
Exercises
175
6
Randomness and Counting
184
6.1
Probabilistic Polynomial Time
185
6.1.1
Basic Modeling Issues
186
6.1.2
Two-Sided Error: The Complexity Class BPP
189
6.1.3
One-Sided Error: The Complexity Classes RP and coRP
193
6.1.4
Zero-Sided Error: The Complexity Class ZPP
199
6.1.5
Randomized Log-Space
199
6.2
Counting
202
6.2.1
Exact Counting
202
6.2.2
Approximate Counting
211
6.2.3
Searching for Unique Solutions
217
6.2.4
Uniform Generation of Solutions
220
Chapter Notes
227
Exercises
230
7
The Bright Side of Hardness
241
7.1
One-Way Functions
242
7.1.1
Generating Hard Instances and One-Way Functions
243
7.1.2
Amplification of Weak One-Way Functions
245
7.1.3
Hard-Core Predicates
250
7.1.4
Reflections on Hardness Amplification
255
7.2
Hard Problems in
E
255
7.2.1
Amplification with Respect to Polynomial-Size Circuits
257
7.2.2
Amplification with Respect to Exponential-Size Circuits
270
Chapter Notes
277
Exercises
278
8
Pseudorandom Generators
284
Introduction
285
8.1
The General Paradigm
288
8.2
General-Purpose Pseudorandom Generators
290
8.2.1
The Basic Definition
291
8.2.2
The Archetypical Application
292
8.2.3
Computational Indistinguishability
295
8.2.4
Amplifying the Stretch Function
299
8.2.5
Constructions
301
8.2.6
Non-uniformly Strong Pseudorandom Generators
304
8.2.7
Stronger Notions and Conceptual Reflections
305
8.3
Derandomization of Time-Complexity Classes
307
8.3.1
Defining Canonical Derandomizers
308
8.3.2
Constructing Canonical Derandomizers
310
8.3.3
Technical Variations and Conceptual Reflections
313
8.4
Space-Bounded Distinguishers
315
8.4.1
Definitional Issues
316
ix
CONTENTS
8.4.2
Two
Constructions
318
8.5
Special-Purpose Generators
325
8.5.1
Pairwise Independence Generators
326
8.5.2
Small-Bias Generators
329
8.5.3
Random Walks on Expanders
332
Chapter Notes
334
Exercises
337
9
Probabilistic Proof Systems
349
Introduction and Preliminaries
350
9.1
Interactive Proof Systems
352
9.1.1
Motivation and Perspective
352
9.1.2
Definition
354
9.1.3
The Power of Interactive Proofs
357
9.1.4
Variants and Finer Structure: An Overview
363
9.1.5
On Computationally Bounded
Provers: An
Overview
366
9.2
Zero-Knowledge Proof Systems
368
9.2.1
Definitional Issues
369
9.2.2
The Power of Zero-Knowledge
372
9.2.3
Proofs of Knowledge- A Parenthetical Subsection
378
93
Probabilistically Checkable Proof Systems
380
9.3.1
Definition
381
9.3.2
The Power of Probabilistically Checkable Proofs
383
9.3.3
PCP
and Approximation
398
9.3.4
More on
PCP
Itself: An Overview
401
Chapter Notes
404
Exercises
406
10
Relaxing the Requirements
416
10.1
Approximation
417
10.1.1
Search or Optimization
418
10.1.2
Decision or Property Testing
423
10.2
Average-Case Complexity
428
10.2.1
The Basic Theory
430
10.2.2
Ramifications
442
Chapter Notes
451
Exercises
453
Epilogue
461
Appendix A: Glossary of Complexity Classes
463
A.1 Preliminaries
463
A.2 Algorithm-Based Classes
464
A.2.1 Time Complexity Classes
464
A.2.2 Space Complexity Classes
467
A3
Circuit-Based Classes
467
Appendix B: On the Quest for Lower Bounds
469
B.1 Preliminaries
469
CONTENTS
B.2
Boolean
Circuit
Complexity
471
В.2.1
Basic Results and Questions
472
B.2.2 Monotone Circuits
473
B.2.3 Bounded-Depth Circuits
473
B.2.4 Formula Size
474
B.3 Arithmetic Circuits
475
B.3.1 Univariate Polynomials
476
B.3.
2
Multivariate Polynomials
476
B.4 Proof Complexity
478
B.4.1 Logical Proof Systems
480
B.4.2 Algebraic Proof Systems
480
B.4.3 Geometric Proof Systems
481
Appendix C: On the Foundations of Modern Cryptography
482
C.I Introduction and Preliminaries
482
С
1.1
The Underlying Principles
483
С
1.2
The Computational Model
485
С
1.3
Organization and Beyond
486
C.2 Computational Difficulty
487
C.2.1 One-Way Functions
487
C.2.2 Hard-Core Predicates
489
C.3 Pseudorandomness
490
C.3.1 Computational Indistinguishability
490
C.3.2 Pseudorandom Generators
491
C.3.3 Pseudorandom Functions
492
C.4 Zero-Knowledge
494
C.4.1 The Simulation Paradigm
494
C.4.2 The Actual Definition
494
C.4.3 A General Result and a Generic Application
495
C.4.4 Definitional Variations and Related Notions
497
C.5 Encryption Schemes
500
C.5.1 Definitions
502
C.5.2 Constructions
504
C.5.3 Beyond Eavesdropping Security
505
C.6 Signatures and Message Authentication
507
C.6.1 Definitions
508
C.6.2 Constructions
509
C.7 General Cryptographic Protocols
511
C.7.
1
The Definitional Approach and Some Models
512
C.7.2 Some Known Results
517
C.7.3 Construction Paradigms and Two Simple Protocols
517
C.7.4 Concluding Remarks
522
Appendix D: Probabilistic Preliminaries and Advanced Topics in
Randomization
523
D.I Probabilistic Preliminaries
523
D.I.I Notational Conventions
523
D.1.2 Three Inequalities
524
xi
CONTENTS
D.2
Hashing
528
D.2.1
Definitions
528
D.2.2
Constructions
529
D.2.3
The Leftover Hash Lemma
529
D.3 Sampling
533
D.3.1 Formal Setting
533
D.3.2 Known Results
534
D.3.3 Hitters
535
D.4 Randomness Extractors
536
D.4.
1
Definitions and Various Perspectives
537
D.4.2 Constructions
541
Appendix E: Explicit Constructions
545
E.I Error-Correcting Codes
546
E
. 1.1
Basic Notions
546
E.
1.2
A Few Popular Codes
547
E.
1.3
Two Additional Computational Problems
551
E.
1.4
A List-Decoding Bound
553
E.2 Expander Graphs
554
E.2.
1
Definitions and Properties
555
E.2.2 Constructions
561
Appendix F: Some Omitted Proofs
566
F.I Proving That VH Reduces to WP
566
F.2 Proving That 1V{
ƒ)
с
AM(O(
ƒ))
Я ЛМ(
f)
572
F.2.1 Emulating
General Interactive
Proofs by AM-Games
572
F.2.2 Linear
Speedup for AM
578
Appendix G:
Some Computational
Problems 583
G.I Graphs
583
G.2
Boolean Formulae
585
G J
Finite Fields, Polynomials, and Vector Spaces
586
G.4 The Determinant and the Permanent
587
G.5 Primes and Composite Numbers
587
Bibliography
589
Index
601
xii
|
| adam_txt |
Contents
List of Figures page
xiii
Preface
xv
Organization and Chapter Summaries
xvii
Acknowledgments
xxiii
1
Introduction and Preliminaries
1
1.1
Introduction
1
1.1.1
A Brief Overview of Complexity Theory
2
1.1.2
Characteristics of Complexity Theory
6
1.1.3
Contents of This Book
8
1.4
Approach and Style of This Book
12
1.5
Standard Notations and Other Conventions
16
1.2
Computational Tasks and Models
17
1.2.1
Representation
18
1.2.2
Computational Tasks
18
1.2.3
Uniform Models (Algorithms)
20
1.2.4
Non-uniform Models (Circuits and Advice)
36
1.2.5
Complexity Classes
42
Chapter Notes
43
2
P, NP, and NP-Completeness
44
2.1
The
Ρ
Versus NP Question
46
2.1.1
The Search Version: Finding Versus Checking
47
2.1.2
The Decision Version: Proving Versus Verifying
50
2.1.3
Equivalence of the Two Formulations
54
2.1.4
Two Technical Comments Regarding NP
55
2.1.5
The Traditional Definition of NP
55
2.1.6
In Support of
Ρ
Different from NP
57
2.1.7
Philosophical Meditations
58
2.2
Polynomial-Time Reductions
58
2.2.1
The General Notion of a Reduction
59
2.2.2
Reducing Optimization Problems to Search Problems
61
2.2.3
Self-Reducibility of Search Problems
63
2.2.4
Digest and General Perspective
67
vii
CONTENTS
2.3 NP-Completeness 67
2.3.1
Definitions
68
2.3.2
The Existence of
NP-Complete Problems 69
2.3.3
Some Natural
NP-Complete Problems 71
2.3.4 NP
Sets That Are Neither
in
Ρ
nor NP-Complete
81
2.3.5
Reflections on Complete Problems
85
2.4
Three Relatively Advanced Topics
87
2.4.1
Promise Problems
87
2.4.2
Optimal Search Algorithms for NP
92
2.4.3
The Class coNP and Its Intersection with NP
94
Chapter Notes
97
Exercises
99
3
Variations on
Ρ
and NP
108
3.1
Non-uniform Polynomial Time (P/poly)
108
3.1.1
Boolean Circuits
109
3.1.2
Machines That Take Advice 111
3.2
The Polynomial-Time Hierarchy (PH)
113
3.2.1
Alternation of Quantifiers
114
3.2.2
Non-deterministic Oracle Machines
117
3.2.3
The P/poly Versus NP Question and PH
119
Chapter Notes
121
Exercises
122
4
More Resources, More Power?
127
4.1
Non-uniform Complexity Hierarchies
128
4.2
Time Hierarchies and Gaps
129
4.2.1
Time Hierarchies
129
4.2.2
Time Gaps and Speedup
136
4.3
Space Hierarchies and Gaps
139
Chapter Notes
139
Exercises
140
5
Space Complexity
143
5.1
General Preliminaries and Issues
144
5.1.1
Important Conventions
144
5.1.2
On the Minimal Amount of Useful Computation Space
145
5.1.3
Time Versus Space
146
5.1.4
Circuit Evaluation
153
5.2
Logarithmic Space
153
5.2.1
The Class
L
154
5.2.2
Log-Space Reductions
154
5.2.3
Log-Space Uniformity and Stronger Notions
155
5.2.4
Undirected Connectivity
155
5.3
Non-deterministic Space Complexity
162
5.3.1
Two Models
162
5.3.2
NL and Directed Connectivity
164
5.3.3
A Retrospective Discussion
171
viii
CONTENTS
5.4 PSPACE and Games 172
Chapter
Notes 175
Exercises
175
6
Randomness and Counting
184
6.1
Probabilistic Polynomial Time
185
6.1.1
Basic Modeling Issues
186
6.1.2
Two-Sided Error: The Complexity Class BPP
189
6.1.3
One-Sided Error: The Complexity Classes RP and coRP
193
6.1.4
Zero-Sided Error: The Complexity Class ZPP
199
6.1.5
Randomized Log-Space
199
6.2
Counting
202
6.2.1
Exact Counting
202
6.2.2
Approximate Counting
211
6.2.3
Searching for Unique Solutions
217
6.2.4
Uniform Generation of Solutions
220
Chapter Notes
227
Exercises
230
7
The Bright Side of Hardness
241
7.1
One-Way Functions
242
7.1.1
Generating Hard Instances and One-Way Functions
243
7.1.2
Amplification of Weak One-Way Functions
245
7.1.3
Hard-Core Predicates
250
7.1.4
Reflections on Hardness Amplification
255
7.2
Hard Problems in
E
255
7.2.1
Amplification with Respect to Polynomial-Size Circuits
257
7.2.2
Amplification with Respect to Exponential-Size Circuits
270
Chapter Notes
277
Exercises
278
8
Pseudorandom Generators
284
Introduction
285
8.1
The General Paradigm
288
8.2
General-Purpose Pseudorandom Generators
290
8.2.1
The Basic Definition
291
8.2.2
The Archetypical Application
292
8.2.3
Computational Indistinguishability
295
8.2.4
Amplifying the Stretch Function
299
8.2.5
Constructions
301
8.2.6
Non-uniformly Strong Pseudorandom Generators
304
8.2.7
Stronger Notions and Conceptual Reflections
305
8.3
Derandomization of Time-Complexity Classes
307
8.3.1
Defining Canonical Derandomizers
308
8.3.2
Constructing Canonical Derandomizers
310
8.3.3
Technical Variations and Conceptual Reflections
313
8.4
Space-Bounded Distinguishers
315
8.4.1
Definitional Issues
316
ix
CONTENTS
8.4.2
Two
Constructions
318
8.5
Special-Purpose Generators
325
8.5.1
Pairwise Independence Generators
326
8.5.2
Small-Bias Generators
329
8.5.3
Random Walks on Expanders
332
Chapter Notes
334
Exercises
337
9
Probabilistic Proof Systems
349
Introduction and Preliminaries
350
9.1
Interactive Proof Systems
352
9.1.1
Motivation and Perspective
352
9.1.2
Definition
354
9.1.3
The Power of Interactive Proofs
357
9.1.4
Variants and Finer Structure: An Overview
363
9.1.5
On Computationally Bounded
Provers: An
Overview
366
9.2
Zero-Knowledge Proof Systems
368
9.2.1
Definitional Issues
369
9.2.2
The Power of Zero-Knowledge
372
9.2.3
Proofs of Knowledge- A Parenthetical Subsection
378
93
Probabilistically Checkable Proof Systems
380
9.3.1
Definition
381
9.3.2
The Power of Probabilistically Checkable Proofs
383
9.3.3
PCP
and Approximation
398
9.3.4
More on
PCP
Itself: An Overview
401
Chapter Notes
404
Exercises
406
10
Relaxing the Requirements
416
10.1
Approximation
417
10.1.1
Search or Optimization
418
10.1.2
Decision or Property Testing
423
10.2
Average-Case Complexity
428
10.2.1
The Basic Theory
430
10.2.2
Ramifications
442
Chapter Notes
451
Exercises
453
Epilogue
461
Appendix A: Glossary of Complexity Classes
463
A.1 Preliminaries
463
A.2 Algorithm-Based Classes
464
A.2.1 Time Complexity Classes
464
A.2.2 Space Complexity Classes
467
A3
Circuit-Based Classes
467
Appendix B: On the Quest for Lower Bounds
469
B.1 Preliminaries
469
CONTENTS
B.2
Boolean
Circuit
Complexity
471
В.2.1
Basic Results and Questions
472
B.2.2 Monotone Circuits
473
B.2.3 Bounded-Depth Circuits
473
B.2.4 Formula Size
474
B.3 Arithmetic Circuits
475
B.3.1 Univariate Polynomials
476
B.3.
2
Multivariate Polynomials
476
B.4 Proof Complexity
478
B.4.1 Logical Proof Systems
480
B.4.2 Algebraic Proof Systems
480
B.4.3 Geometric Proof Systems
481
Appendix C: On the Foundations of Modern Cryptography
482
C.I Introduction and Preliminaries
482
С
1.1
The Underlying Principles
483
С
1.2
The Computational Model
485
С
1.3
Organization and Beyond
486
C.2 Computational Difficulty
487
C.2.1 One-Way Functions
487
C.2.2 Hard-Core Predicates
489
C.3 Pseudorandomness
490
C.3.1 Computational Indistinguishability
490
C.3.2 Pseudorandom Generators
491
C.3.3 Pseudorandom Functions
492
C.4 Zero-Knowledge
494
C.4.1 The Simulation Paradigm
494
C.4.2 The Actual Definition
494
C.4.3 A General Result and a Generic Application
495
C.4.4 Definitional Variations and Related Notions
497
C.5 Encryption Schemes
500
C.5.1 Definitions
502
C.5.2 Constructions
504
C.5.3 Beyond Eavesdropping Security
505
C.6 Signatures and Message Authentication
507
C.6.1 Definitions
508
C.6.2 Constructions
509
C.7 General Cryptographic Protocols
511
C.7.
1
The Definitional Approach and Some Models
512
C.7.2 Some Known Results
517
C.7.3 Construction Paradigms and Two Simple Protocols
517
C.7.4 Concluding Remarks
522
Appendix D: Probabilistic Preliminaries and Advanced Topics in
Randomization
523
D.I Probabilistic Preliminaries
523
D.I.I Notational Conventions
523
D.1.2 Three Inequalities
524
xi
CONTENTS
D.2
Hashing
528
D.2.1
Definitions
528
D.2.2
Constructions
529
D.2.3
The Leftover Hash Lemma
529
D.3 Sampling
533
D.3.1 Formal Setting
533
D.3.2 Known Results
534
D.3.3 Hitters
535
D.4 Randomness Extractors
536
D.4.
1
Definitions and Various Perspectives
537
D.4.2 Constructions
541
Appendix E: Explicit Constructions
545
E.I Error-Correcting Codes
546
E
. 1.1
Basic Notions
546
E.
1.2
A Few Popular Codes
547
E.
1.3
Two Additional Computational Problems
551
E.
1.4
A List-Decoding Bound
553
E.2 Expander Graphs
554
E.2.
1
Definitions and Properties
555
E.2.2 Constructions
561
Appendix F: Some Omitted Proofs
566
F.I Proving That VH Reduces to WP
566
F.2 Proving That 1V{
ƒ)
с
AM(O(
ƒ))
Я ЛМ(
f)
572
F.2.1 Emulating
General Interactive
Proofs by AM-Games
572
F.2.2 Linear
Speedup for AM
578
Appendix G:
Some Computational
Problems 583
G.I Graphs
583
G.2
Boolean Formulae
585
G J
Finite Fields, Polynomials, and Vector Spaces
586
G.4 The Determinant and the Permanent
587
G.5 Primes and Composite Numbers
587
Bibliography
589
Index
601
xii |
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| dewey-full | 511.3/52 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 511 - General principles of mathematics |
| dewey-raw | 511.3/52 |
| dewey-search | 511.3/52 |
| dewey-sort | 3511.3 252 |
| dewey-tens | 510 - Mathematics |
| discipline | Informatik Mathematik |
| discipline_str_mv | Informatik Mathematik |
| edition | 1. publ. |
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| index_date | 2024-07-02T20:55:42Z |
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| spelling | Goldreich, Oded 1957- Verfasser (DE-588)120549255 aut Computational complexity a conceptual perspective Oded Goldreich 1. publ. Cambridge [u.a.] Cambridge Univ. Press 2008 XXIV, 606 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Includes bibliographical references and index Computational complexity Turing machines Turing-Maschine (DE-588)4203525-9 gnd rswk-swf Berechnungskomplexität (DE-588)4134751-1 gnd rswk-swf Berechnungskomplexität (DE-588)4134751-1 s DE-604 Turing-Maschine (DE-588)4203525-9 s http://www.loc.gov/catdir/enhancements/fy0811/2008006750-b.html Contributor biographical information http://www.loc.gov/catdir/enhancements/fy0811/2008006750-d.html Publisher description http://www.loc.gov/catdir/enhancements/fy0811/2008006750-t.html Table of contents only Digitalisierung UB Bayreuth application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=016510317&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Goldreich, Oded 1957- Computational complexity a conceptual perspective Computational complexity Turing machines Turing-Maschine (DE-588)4203525-9 gnd Berechnungskomplexität (DE-588)4134751-1 gnd |
| subject_GND | (DE-588)4203525-9 (DE-588)4134751-1 |
| title | Computational complexity a conceptual perspective |
| title_auth | Computational complexity a conceptual perspective |
| title_exact_search | Computational complexity a conceptual perspective |
| title_exact_search_txtP | Computational complexity a conceptual perspective |
| title_full | Computational complexity a conceptual perspective Oded Goldreich |
| title_fullStr | Computational complexity a conceptual perspective Oded Goldreich |
| title_full_unstemmed | Computational complexity a conceptual perspective Oded Goldreich |
| title_short | Computational complexity |
| title_sort | computational complexity a conceptual perspective |
| title_sub | a conceptual perspective |
| topic | Computational complexity Turing machines Turing-Maschine (DE-588)4203525-9 gnd Berechnungskomplexität (DE-588)4134751-1 gnd |
| topic_facet | Computational complexity Turing machines Turing-Maschine Berechnungskomplexität |
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