Complexity and real computation:
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| Format: | Book |
|---|---|
| Language: | English |
| Published: |
New York ; Berlin ; Heidelberg ; Barcelona ; Budapest ; Hong Kong ; London ; Milan ; Paris ; Santa Clara ; Singapore ; Tokyo
Springer
1997
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| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Item Description: | Literaturverz. S. 431 - 445 |
| Physical Description: | XVI, 453 S. Ill., graph. Darst. 25 cm |
| ISBN: | 0387982817 |
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MARC
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| 084 | |a 28 |2 sdnb | ||
| 245 | 1 | 0 | |a Complexity and real computation |c Lenore Blum ... Foreword by Richard M. Karp |
| 264 | 1 | |a New York ; Berlin ; Heidelberg ; Barcelona ; Budapest ; Hong Kong ; London ; Milan ; Paris ; Santa Clara ; Singapore ; Tokyo |b Springer |c 1997 | |
| 300 | |a XVI, 453 S. |b Ill., graph. Darst. |c 25 cm | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 500 | |a Literaturverz. S. 431 - 445 | ||
| 650 | 4 | |a Informatik | |
| 650 | 4 | |a Computer science | |
| 650 | 4 | |a Computational complexity | |
| 650 | 4 | |a Real-time data processing | |
| 650 | 4 | |a Computer algorithms | |
| 650 | 0 | 7 | |a Komplexitätstheorie |0 (DE-588)4120591-1 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Berechnungskomplexität |0 (DE-588)4134751-1 |2 gnd |9 rswk-swf |
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| 689 | 0 | |5 DE-604 | |
| 689 | 1 | 0 | |a Komplexitätstheorie |0 (DE-588)4120591-1 |D s |
| 689 | 1 | |8 1\p |5 DE-604 | |
| 700 | 1 | |a Blum, Lenore |e Sonstige |4 oth | |
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Record in the Search Index
| _version_ | 1807505207669555200 |
|---|---|
| adam_text |
CONTENTS
FOREWORD
V
PREFACE
IX
I
BASIC
DEVELOPMENT
1
INTRODUCTION
3
1.1
AIM
.
3
1.2
SEVEN
EXAMPLES
.
4
1.2.1
IS
THE
MANDELBROT
SET
DECIDABLE?
.
4
1.2.2
EXAMPLE
OF
THE
JULIA
SET
OF
T(Z)
=
Z
2
+
4
.
8
1.2.3
NEWTON
'
S
METHOD
.
10
1.2.4
THE
KNAPSACK
PROBLEM
.
12
1.2.5
THE
HILBERT
NULLSTELLENSATZ
AS
A
DECISION
PROBLEM
.
.
.
15
1.2.6
FEASIBILITY
OF
REAL
POLYNOMIALS
.
17
1.2.7
LINEAR
PROGRAMMING
AND
INTEGER
PROGRAMMING
.
18
1.3
THE
CLASSICAL
THEORY
OF
COMPUTATION
.
20
1.4
TOWARD
A
MATHEMATICAL
FOUNDATION
OF
NUMERICAL
ANALYSIS
.
.
22
1.5
CLASSICAL
COMPLEXITY
THEORY
AND
ITS
EXTENSION
.
24
1.6
COMPLEXITY
THEORY
IN
NUMERICAL
ANALYSIS
.
28
1.7
SUMMARY
.
30
1.8
BRIEF
HISTORY
AND
COMPARISON
WITH
OTHER
MODELS
OF
COMPUTATION
.
31
XII
C
ONTENTS
2
DEFINITIONS
AND
FIRST
PROPERTIES
OF
COMPUTATION
37
2.1
THE
MODEL
OF
COMPUTATION:
THE
FINITE-DIMENSIONAL
CASE
.
.
.
38
2.2
THE
INPUT-OUTPUT
MAP,
HALTING
SET,
AND
THE
COMPUTING
ENDOMORPHISM
.
44
2.3
HALTING
SETS
AND
COMPUTABLE
MAPS
.
48
2.4
THE
MANDELBROT
SET
IS
UNDECIDABLE
.
55
2.5
THE
CANONICAL
PATH
CONSTRUCTION
.
56
2.6
THE
REGISTER
EQUATIONS
AND
SUCCINCT
DESCRIPTIONS
.
58
2.7
MORE
SUCCINCT
DESCRIPTIONS
.
63
2.8
ADDITIONAL
COMMENTS
AND
BIBLIOGRAPHICAL
REMARKS
.
67
3
COMPUTATION
OVER
A
RING
69
3.1
7?
00
AND
R
QO
.
70
3.2
MACHINES
OVER
R
.
71
3.3
PATH
DECOMPOSITION
AND
REDUCTION
TO
THE
FINITE-DIMENSIONAL
CASE
.
74
3.4
THE
REGISTER
EQUATIONS
.
77
3.5
PRODUCT
SPACES,
CODES
AND
UNIVERSAL
MACHINES
.
79
3.6
ADDITIONAL
COMMENTS
AND
BIBLIOGRAPHICAL
REMARKS
.
81
4
DECISION
PROBLEMS
AND
COMPLEXITY
OVER
A
RING
83
4.1
DECISION
PROBLEMS
.
83
4.2
COMPLEXITY
AND
THE
CLASS
P
.
86
4.3
POLYNOMIAL
TIME
REDUCTIONS
.
90
4.4
MANAGEMENT,
MACHINES
AND
ALGORITHMS
.
93
4.5
ADDITIONAL
COMMENTS
AND
BIBLIOGRAPHICAL
REMARKS
.
96
5
THE
CLASS
NP
AND
NP-COMPLETE
PROBLEMS
99
5.1
THE
CLASS
NP
.
100
5.2
IMPORTANT
NP
PROBLEMS
.
103
5.3
NP-COMPLETENESS
.
104
5.4
NP-COMPLETE
PROBLEMS
OVER
C,
R,
AND
1
.
104
5.5
NP-COMPLETE
PROBLEMS
OVER
Z2
.
107
5.6
ADDITIONAL
COMMENTS
AND
BIBLIOGRAPHICAL
REMARKS
.
110
6
INTEGER
MACHINES
113
6.1
POLYNOMIAL
EQUIVALENCE
OF
MACHINES
OVER
Z
AND
Z2
.
113
6.2
SOME
RESULTS
ON
LINEAR
INEQUALITIES
.
116
6.3
THE
COMPLEXITY
OF
INTEGER
PROGRAMMING
.
121
6.4
ADDITIONAL
COMMENTS
AND
BIBLIOGRAPHICAL
REMARKS
.
124
7
ALGEBRAIC
SETTINGS
FOR
THE
PROBLEM
"
P
/
NP?
"
125
7.1
STATEMENT
OF
MAIN
THEOREMS
.
125
7.2
ELIMINATING
CONSTANTS:
EASY
CASES
.
127
7.3
WITNESS
THEOREM
.
129
C
ONTENTS
XIII
APPENDIX
TO
SECTION
7.3
.
135
7.4
ELIMINATION
OF
CONSTANTS:
GENERAL
CASE
.
136
7.5
TWENTY
QUESTIONS
.
137
7.6
PROOF
OF
THEOREMS
2
AND
3
.
140
7.7
MAIN
THEOREM,
AN
ALGEBRAIC
PROOF
OF
THE
CONVERSE
.
141
7.8
MAIN
THEOREM,
A
MODEL-THEORETIC
PROOF
OF
THE
CONVERSE
.
.
.
143
7.9
ADDITIONAL
COMMENTS
AND
BIBLIOGRAPHICAL
REMARKS
.
145
APPENDIX
A
A.L
BASIC
NOTIONS
OF
ALGEBRAIC
GEOMETRY
.
147
A.2 ADDITIONAL
COMMENTS
AND
BIBLIOGRAPHICAL
REMARKS
.
149
II
SOME
GEOMETRY
OF
NUMERICAL
ALGORITHMS
8
NEWTON
'
S
METHOD
153
8.1
APPROXIMATE
ZEROS
.
154
8.2
POINT
ESTIMATES
FOR
APPROXIMATE
ZEROS
.
159
8.3
ADDITIONAL
COMMENTS
AND
BIBLIOGRAPHICAL
REMARKS
.
168
9
FUNDAMENTAL
THEOREM
OF
ALGEBRA:
COMPLEXITY
ASPECTS
169
9.1
THE
FUNDAMENTAL
THEOREM
OF
ALGEBRA
.
169
9.2 A
HOMOTOPY
METHOD
.
172
9.3
WHERE
TO
BEGIN
THE
HOMOTOPY
.
178
9.4
THE
ALGORITHM
AND
ITS
COMPLEXITY
.
184
9.5
ADDITIONAL
COMMENTS
AND
BIBLIOGRAPHICAL
REMARKS
.
185
10
BEZOUT
'
S
THEOREM
187
10.1
THE
FUNDAMENTAL
THEOREM
OF
ALGEBRA
REVISITED
.
187
10.2
PROJECTIVE
SPACE
.
190
10.3
THE
VARIETIES
V,
S',
AND
S
.
193
10.4
THE
DISCRIMINANT
VARIETY
IN
ONE
VARIABLE
.
194
10.5
BEZOUT
'
S
THEOREM
.
198
10.6
ADDITIONAL
COMMENTS
AND
BIBLIOGRAPHICAL
REMARKS
.
199
11
CONDITION
NUMBERS
AND
THE
LOSS
OF
PRECISION
OF
LINEAR
EQUATIONS
201
11.1
THE
ECKART-YOUNG
THEOREM
.
202
11.2
PROBABILITIES
AND
INTEGRALS
.
204
11.3
SOME
INTEGRATION
FORMULAS
.
205
11.4
A
LINEAR
ALGEBRA
ESTIMATE
.
209
11.5
THE
MAIN
THEOREMS
FOR
THE
REALS
.
210
11.6
THE
MAIN
THEOREMS
FOR
THE
COMPLEX
NUMBERS
.
213
11.7
ADDITIONAL
COMMENTS
AND
BIBLIOGRAPHICAL
REMARKS
.
214
12
THE
CONDITION
NUMBER
FOR
NONLINEAR
PROBLEMS
217
12.1
UNITARY
INVARIANCE
.
217
XIV
C
ONTENTS
12.2
HERMITIAN
STRUCTURES
AND
DISTANCES
IN
PROJECTIVE
SPACE
.
222
12.3
THE
CONDITION
NUMBER
(NONLINEAR)
.
227
12.4
THE
CONDITION
NUMBER
THEOREM
.
232
12.5
ADDITIONAL
COMMENTS
AND
BIBLIOGRAPHICAL
REMARKS
.
236
13
THE
CONDITION
NUMBER
IN
237
13.1
INTEGRATION
ON
MANIFOLDS
.
237
13.2
A
GENERAL
INTEGRAL
FORMULA
.
240
13.3
INTEGRATION
IN
V
AND
THE
AVERAGE
NUMBER
OF
REAL
ROOTS
.
244
13.4
THE
CONDITION
NUMBER
IN
YY
+1)
.
248
13.5
A
LINEAR
ALGEBRA
ESTIMATE
AND
THE
DISTRIBUTION
OF
THE
CONDITION
NUMBER
.
250
13.6
THE
DISTRIBUTION
OF
THE
NORMALIZED
CONDITION
NUMBER
FOR
P(W
W
)
.
255
13.7
ADDITIONAL
COMMENTS
AND
BIBLIOGRAPHICAL
REMARKS
.
258
14
COMPLEXITY
AND
THE
CONDITION
NUMBER
261
14.1
NEWTON
'
S
METHOD
IN
PROJECTIVE
SPACE
.
261
14.2
THE
HIGHER
DERIVATIVE
ESTIMATE
.
267
14.3
COMPLEXITY
OF
HOMOTOPY
METHODS
.
271
14.4
ADDITIONAL
COMMENTS
AND
BIBLIOGRAPHICAL
REMARKS
.
273
IS
LINEAR
PROGRAMMING
275
15.1
MACHINES
OVER
Q
.
275
15.2
THE
BARRIER
METHOD
IN
LINEAR
PROGRAMMING
.
277
15.3
LINEAR
PROGRAMMING
OVER
Q
.
286
15.4
POLYNOMIAL
COST
.
289
15.5
ON
THE
COST
OF
INVERTING
A
MATRIX
.
292
15.6
ADDITIONAL
COMMENTS
AND
BIBLIOGRAPHICAL
REMARKS
.
296
APPENDIX
B
B.L
THE
MAIN
THEOREM
OF
ELIMINATION
THEORY
.
297
B.2 ADDITIONAL
COMMENTS
AND
BIBLIOGRAPHICAL
REMARKS
.
299
III
COMPLEXITY
CLASSES
OVER
THE
REALS
16
DETERMINISTIC
LOWER
BOUNDS
303
16.1
A
GEOMETRIC
UPPER
BOUND
.
303
16.2
A
COMPLEXITY
LOWER
BOUND
.
309
16.3
ON
THE
NUMBER
OF
CONNECTED
COMPONENTS
OF
SEMI-ALGEBRAIC
SETS
.
312
16.4
ADDITIONAL
COMMENTS
AND
BIBLIOGRAPHICAL
REMARKS
.
315
17
PROBABILISTIC
MACHINES
317
17.1
MACHINES
THAT
FLIP
COINS
.
318
C
ONTENTS
XV
17.2
SIMULATING
PROBABILISTIC
TREES
.
320
17.3
TWO
BOUNDS
FOR
THE
TAIL
OF
THE
BINOMIAL
DISTRIBUTION
.
323
17.4
APPROXIMATING
THE
VOLUME
OF
BOUNDED
SEMI-ALGEBRAIC
SETS
.
326
17.5
MACHINES
THAT
PICK
REAL
NUMBERS
IN
[0,1]
.
330
17.6
SIMULATING
PROBABILISTIC
MACHINES
.
332
17.7
ADDITIONAL
COMMENTS
AND
BIBLIOGRAPHICAL
REMARKS
.
333
18
PARALLEL
COMPUTATIONS
335
18.1
SOME
OLD
PROBLEMS
REVISITED
.
335
18.2
A
PARALLEL
MODEL
OF
COMPUTATION
.
342
18.3
DETERMINISTIC
UPPER
BOUNDS
FOR
NP
R
.
348
18.4
ALGEBRAIC
CIRCUITS
.
349
18.5
THE
CLASS
NC
R
.
352
18.6
ADDITIONAL
COMMENTS
AND
BIBLIOGRAPHICAL
REMARKS
.
356
19
SOME
SEPARATIONS
OF
COMPLEXITY
CLASSES
359
19.1
A
SEPARATION
RESULT
.
359
19.2
LOWER
BOUNDS
FOR
PARALLEL
TIME
.
365
19.3
COMPLETENESS
IN
P
R
.
366
19.4
DIGITAL
NONDETERMINISM
.
370
19.5
THE
COMPLEXITY
OF
THE
KNAPSACK
PROBLEM
.
371
19.6
ADDITIONAL
COMMENTS
AND
BIBLIOGRAPHICAL
REMARKS
.
374
20
WEAK
MACHINES
377
20.1
A
RESTRICTION
ON
THE
NUMBER
OF
MULTIPLICATIONS
.
377
20.2
A
CHARACTERIZATION
OF
DIGITAL
NONDETERMINISNM
.
381
20.3
LINEAR
PROGRAMMING
AND
DIGITAL
NONDETERMINISM
.
383
20.4
ADDITIONAL
COMMENTS
AND
BIBLIOGRAPHICAL
REMARKS
.
384
21
ADDITIVE
MACHINES
385
21.1
ADDITIVE
MACHINES
AND
COMPLEXITY
CLASSES
.
385
21.2
THE
POLYNOMIAL
HIERARCHY
.
389
21.3
ON
THE
DEFINITION
OF
THE
POLYNOMIAL
HIERARCHY
.
393
21.4
THE
POLYNOMIAL
HIERARCHY
FOR
UNRESTRICTED
MACHINES
.
398
21.5
ADDITIONAL
COMMENTS
AND
BIBLIOGRAPHICAL
REMARKS
.
399
22
NONUNIFORM
COMPLEXITY
CLASSES
401
22.1
COMPLEXITY
CLASSES
DEFINED
BY
ADVICE
FUNCTIONS
.
401
22.2
BOOLEAN
PARTS
.
404
22.3
ADDITIONAL
COMMENTS
AND
BIBLIOGRAPHICAL
REMARKS
.
408
23
DESCRIPTIVE
COMPLEXITY
411
23.1
VOCABULARIES,
STRUCTURES,
AND
FIRST-ORDER
LOGIC
.
412
23.2
LOGICS
ON
R-STRUCTURES
.
415
23.3
CAPTURING
P
R
WITH
FIXED
POINT
FIRST-ORDER
LOGIC
.
420
23.4
CAPTURING
NP
R
WITH
EXISTENTIAL
SECOND-ORDER
LOGIC
.
426
XVI
C
ONTENTS
23.5
ADDITIONAL
COMMENTS
AND
BIBLIOGRAPHICAL
REMARKS
.
429
REFERENCES
431
INDEX
447 |
| adam_txt | |
| any_adam_object | 1 |
| any_adam_object_boolean | |
| building | Verbundindex |
| bvnumber | BV023514423 |
| callnumber-first | Q - Science |
| callnumber-label | QA76 |
| callnumber-raw | QA76.C5474 1998 |
| callnumber-search | QA76.C5474 1998 |
| callnumber-sort | QA 276 C5474 41998 |
| callnumber-subject | QA - Mathematics |
| classification_rvk | ST 120 |
| ctrlnum | (OCoLC)832750887 (DE-599)BVBBV023514423 |
| dewey-full | 511.321 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 511 - General principles of mathematics |
| dewey-raw | 511.3 21 |
| dewey-search | 511.3 21 |
| dewey-sort | 3511.3 221 |
| dewey-tens | 510 - Mathematics |
| discipline | Informatik Mathematik |
| discipline_str_mv | Informatik Mathematik |
| format | Book |
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| id | DE-604.BV023514423 |
| illustrated | Illustrated |
| index_date | 2024-07-02T22:31:36Z |
| indexdate | 2024-08-16T01:21:31Z |
| institution | BVB |
| isbn | 0387982817 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-016835370 |
| oclc_num | 832750887 |
| open_access_boolean | |
| owner | DE-521 |
| owner_facet | DE-521 |
| physical | XVI, 453 S. Ill., graph. Darst. 25 cm |
| publishDate | 1997 |
| publishDateSearch | 1997 |
| publishDateSort | 1997 |
| publisher | Springer |
| record_format | marc |
| spelling | Complexity and real computation Lenore Blum ... Foreword by Richard M. Karp New York ; Berlin ; Heidelberg ; Barcelona ; Budapest ; Hong Kong ; London ; Milan ; Paris ; Santa Clara ; Singapore ; Tokyo Springer 1997 XVI, 453 S. Ill., graph. Darst. 25 cm txt rdacontent n rdamedia nc rdacarrier Literaturverz. S. 431 - 445 Informatik Computer science Computational complexity Real-time data processing Computer algorithms Komplexitätstheorie (DE-588)4120591-1 gnd rswk-swf Berechnungskomplexität (DE-588)4134751-1 gnd rswk-swf Berechnungskomplexität (DE-588)4134751-1 s DE-604 Komplexitätstheorie (DE-588)4120591-1 s 1\p DE-604 Blum, Lenore Sonstige oth DNB Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=016835370&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 | Complexity and real computation Informatik Computer science Computational complexity Real-time data processing Computer algorithms Komplexitätstheorie (DE-588)4120591-1 gnd Berechnungskomplexität (DE-588)4134751-1 gnd |
| subject_GND | (DE-588)4120591-1 (DE-588)4134751-1 |
| title | Complexity and real computation |
| title_auth | Complexity and real computation |
| title_exact_search | Complexity and real computation |
| title_exact_search_txtP | Complexity and real computation |
| title_full | Complexity and real computation Lenore Blum ... Foreword by Richard M. Karp |
| title_fullStr | Complexity and real computation Lenore Blum ... Foreword by Richard M. Karp |
| title_full_unstemmed | Complexity and real computation Lenore Blum ... Foreword by Richard M. Karp |
| title_short | Complexity and real computation |
| title_sort | complexity and real computation |
| topic | Informatik Computer science Computational complexity Real-time data processing Computer algorithms Komplexitätstheorie (DE-588)4120591-1 gnd Berechnungskomplexität (DE-588)4134751-1 gnd |
| topic_facet | Informatik Computer science Computational complexity Real-time data processing Computer algorithms Komplexitätstheorie Berechnungskomplexität |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=016835370&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| work_keys_str_mv | AT blumlenore complexityandrealcomputation |