The complexity theory companion:
Gespeichert in:
| Hauptverfasser: | , |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Berlin [u.a.]
Springer
2002
|
| Schriftenreihe: | Texts in theoretical computer science
|
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | XIII, 369 S. |
| ISBN: | 3540674195 |
Internformat
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Datensatz im Suchindex
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|---|---|
| adam_text |
LANE A. HEMASPAANDRA * MITSUNORI OGIHARA THE COMPLEXITY THEORY COMPANION
WITH 43 FIGURES SPRINGER CONTENTS PREFACE VII INVITATION VII USAGE VIII
1. THE SELF-REDUCIBILITY TECHNIQUE 1 1.1 GEM: THERE ARE NO SPARSE
NP-COMPLETE SETS UNLESS P=NP 2 1.2 THE TURING CASE 18 1.3 THE CASE OF
MERELY PUTTING SPARSE SETS IN NP - P: THE HARTMANIS-IMMERMAN-SEWELSON
ENCODING 22 1.4 OPEN ISSUE: DOES THE DISJUNCTIVE CASE HOLD? 26 1.5
BIBLIOGRAPHIC NOTES 26 2. THE ONE-WAY FUNCTION TECHNIQUE 31 2.1 GEM:
CHARACTERIZING THE EXISTENCE OF ONE-WAY FUNCTIONS . . 32 2.2 UNAMBIGUOUS
ONE-WAY FUNCTIONS EXIST IF AND ONLY IF BOUNDED-AMBIGUITY ONE-WAY
FUNCTIONS EXIST 35 2.3 STRONG, TOTAL, COMMUTATIVE, ASSOCIATIVE ONE-WAY
FUNCTIONS EXIST IF AND ONLY IF ONE-WAY FUNCTIONS EXIST. 36 2.4 OPEN
ISSUE: LOW-AMBIGUITY, COMMUTATIVE, ASSOCIATIVE ONE-WAY FUNCTIONS? 42 2.5
BIBLIOGRAPHIC NOTES 43 3. THE TOURNAMENT DIVIDE AND CONQUER TECHNIQUE 45
3.1 GEM: THE SEMI-FEASIBLE SETS HAVE SMALL CIRCUITS 45 3.2 OPTIMAL
ADVICE FOR THE SEMI-FEASIBLE SETS 48 3.3 UNIQUE^SOLUTIONS COLLAPSE THE
POLYNOMIAL HIERARCHY 56 3.4 OPEN ISSUE: ARE THE SEMI-FEASIBLE SETS IN
P/LINEAR? 63 3.5 BIBLIOGRAPHIC NOTES 63 4. THE ISOLATION TECHNIQUE 67
4.1 GEM: ISOLATING A UNIQUE SOLUTION 68 4.2 TODA'S THEOREM: PH C P PP 72
4.3 NL/POLY = UL/POLY 82 XII CONTENTS 4.4 OPEN ISSUE: DO AMBIGUOUS AND
UNAMBIGUOUS NONDETERMINISM COINCIDE? 87 4.5 BIBLIOGRAPHIC NOTES 87 5.
THE WITNESS REDUCTION TECHNIQUE 91 5.1 FRAMING THE QUESTION: IS #P
CLOSED UNDER PROPER SUBTRACTION? 91 5.2 GEM: A COMPLEXITY THEORY FOR
FEASIBLE CLOSURE PROPERTIES OF #P 93 5.3 INTERMEDIATE POTENTIAL CLOSURE
PROPERTIES 99 5.4 A COMPLEXITY THEORY FOR FEASIBLE CLOSURE PROPERTIES OF
OPTP 103 5.5 OPEN ISSUE: CHARACTERIZING CLOSURE UNDER PROPER DECREMENT
105 5.6 BIBLIOGRAPHIC NOTES 106 6. THE POLYNOMIAL INTERPOLATION
TECHNIQUE 109 6.1 GEM: INTERACTIVE PROTOCOLS FOR THE PERMANENT 110 6.2
ENUMERATORS FOR THE PERMANENT 119 6.3 IP = PSPACE 122 6.4 MIP = NEXP 133
6.5 OPEN ISSUE: THE POWER OF THE PROVERS 163 6.6 BIBLIOGRAPHIC NOTES 163
7. THE NONSOLVABLE GROUP TECHNIQUE 167 7.1 GEM: WIDTH-5 BRANCHING
PROGRAMS CAPTURE NONUNIFORM-NC 1 168 7.2 WIDTH-5 BOTTLENECK MACHINES
CAPTURE PSPACE 176 7.3 WIDTH-2 BOTTLENECK COMPUTATION 181 7.4 OPEN
ISSUE: HOW COMPLEX IS MAJORITY-BASED PROBABILISTIC SYMMETRIC BOTTLENECK
COMPUTATION? 192 7.5 BIBLIOGRAPHIC NOTES 192 8. THE RANDOM RESTRICTION
TECHNIQUE 197 8.1 GEM: THE RANDOM RESTRICTION TECHNIQUE AND A
POLYNOMIAL-SIZE LOWER BOUND FOR PARITY 197 8.2 AN EXPONENTIAL-SIZE LOWER
BOUND FOR PARITY 207 8.3 PH AND PSPACE DIFFER WITH PROBABILITY ONE . .
.* 218 8.4 ORACLES THAT MAKE THE POLYNOMIAL HIERARCHY INFINITE 222 8.5
OPEN ISSUE: IS THE POLYNOMIAL HIERARCHY INFINITE WITH PROBABILITY ONE?
231 8.6 BIBLIOGRAPHIC NOTES 231 CONTENTS XIII 9. THE POLYNOMIAL
TECHNIQUE 235 9.1 GEM: THE POLYNOMIAL TECHNIQUE 236 9.2 CLOSURE
PROPERTIES OF PP 241 9.3 THE PROBABILISTIC LOGSPACE HIERARCHY COLLAPSES
252 9.4 OPEN ISSUE: IS PP CLOSED UNDER POLYNOMIAL-TIME TURING
REDUCTIONS? 259 9.5 BIBLIOGRAPHIC NOTES 260 A. A ROGUES' GALLERY OF
COMPLEXITY CLASSES 263 A.I P: DETERMINISM 264 A.2 NP: NONDETERMINISM 266
A.3 ORACLES AND RELATIVIZED WORLDS 268 A.4 THE POLYNOMIAL HIERARCHY AND
POLYNOMIAL SPACE: THE POWER OF QUANTIFIERS 270 A.5 E, NE, EXP, AND NEXP
. 274 A.6 P/POLY: SMALL CIRCUITS 276 A.7. L, NL, ETC.: LOGSPACE CLASSES
277 A.8 NC, AC, LOGCFL: CIRCUIT CLASSES 279 A.9 UP, FEWP, AND US:
AMBIGUITY-BOUNDED COMPUTATION AND UNIQUE COMPUTATION 281 A.10 #P:
COUNTING SOLUTIONS .' 286 A.LL ZPP, RP, CORP, AND BPP: ERROR-BOUNDED
PROBABILISM 288 A.12 PP, C = P, AND SPP: COUNTING CLASSES 290 A. 13 FP,
NPSV, AND NPMV: DETERMINISTIC AND NONDETERMINISTIC FUNCTIONS 291 A. 14
P-SEL: SEMI-FEASIBLE COMPUTATION 294 A.15 P, MODFCP: MODULO-BASED
COMPUTATION 297 A. 16 SPANP, OPTP: OUTPUT-CARDINALITY AND OPTIMIZATION
FUNCTION CLASSES 297 A. 17 IP AND MIP: INTERACTIVE PROOF CLASSES 299
A.18 PBP, SF, SSF: BRANCHING PROGRAMS AND BOTTLENECK COMPUTATION 300 B.
A ROGUES' GALLERY OF REDUCTIONS 305 B.I REDUCTION DEFINITIONS: N , PT
, 305 B.2 SHORTHANDS: R AND E 307 B.3 FACTS ABOUT REDUCTIONS 307 B.4
CIRCUIT-BASED REDUCTIONS: NC FE AND AC FC 308 B.5 BIBLIOGRAPHIC NOTES
308 REFERENCES 309 INDEX 335 |
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| discipline | Informatik Psychologie |
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| id | DE-604.BV013992789 |
| illustrated | Not Illustrated |
| indexdate | 2024-08-01T00:27:47Z |
| institution | BVB |
| isbn | 3540674195 |
| language | English |
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| physical | XIII, 369 S. |
| publishDate | 2002 |
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| spelling | Hemaspaandra, Lane A. Verfasser aut The complexity theory companion Lane A. Hemaspaandra ; Mitsunori Ogihara Berlin [u.a.] Springer 2002 XIII, 369 S. txt rdacontent n rdamedia nc rdacarrier Texts in theoretical computer science Algoritmen gtt Complexiteit gtt Complexité de calcul (Informatique) Computational complexity Komplexitätstheorie (DE-588)4120591-1 gnd rswk-swf Komplexitätstheorie (DE-588)4120591-1 s DE-604 Ogihara, Mitusnori 1963- Verfasser (DE-588)123203260 aut HEBIS Datenaustausch Darmstadt application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=009577901&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Hemaspaandra, Lane A. Ogihara, Mitusnori 1963- The complexity theory companion Algoritmen gtt Complexiteit gtt Complexité de calcul (Informatique) Computational complexity Komplexitätstheorie (DE-588)4120591-1 gnd |
| subject_GND | (DE-588)4120591-1 |
| title | The complexity theory companion |
| title_auth | The complexity theory companion |
| title_exact_search | The complexity theory companion |
| title_full | The complexity theory companion Lane A. Hemaspaandra ; Mitsunori Ogihara |
| title_fullStr | The complexity theory companion Lane A. Hemaspaandra ; Mitsunori Ogihara |
| title_full_unstemmed | The complexity theory companion Lane A. Hemaspaandra ; Mitsunori Ogihara |
| title_short | The complexity theory companion |
| title_sort | the complexity theory companion |
| topic | Algoritmen gtt Complexiteit gtt Complexité de calcul (Informatique) Computational complexity Komplexitätstheorie (DE-588)4120591-1 gnd |
| topic_facet | Algoritmen Complexiteit Complexité de calcul (Informatique) Computational complexity Komplexitätstheorie |
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