Completeness and reduction in algebraic complexity theory:
Saved in:
| Main Author: | |
|---|---|
| Format: | Thesis Book |
| Language: | English |
| Published: |
Berlin [u.a.]
Springer
2000
|
| Series: | Algorithms and computation in mathematics
7 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | XII, 168 S. graph. Darst. |
| ISBN: | 3540667520 |
Staff View
MARC
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| 245 | 1 | 0 | |a Completeness and reduction in algebraic complexity theory |c Peter Bürgisser |
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Record in the Search Index
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| adam_text | Contents
1 Introduction 1
1.1 Classical Model 1
1.2 Blum Shub Smale Model 3
1.3 Valiant s Model 4
1.4 Overview of Main Results 6
2 Valiant s Algebraic Model of NP Completeness 11
2.1 The Complexity Classes VP and VNP 11
2.2 Completeness of the Permanent Family 16
2.2.1 p Definability and Formula Size 16
2.2.2 Universality of the Permanent 19
2.2.3 Completeness of the Permanent 21
2.3 Closure Properties 25
2.4 Parallel Complexity 30
2.5 Completeness of the Determinant Family 34
3 Some Complete Families of Polynomials 37
3.1 Generating Functions of Graph Properties 37
3.2 p Computable Families 39
3.3 VNP Complete Families 41
3.3.1 Matchings 42
3.3.2 Cliques 43
3.3.3 Cycle Format Polynomials 44
3.3.4 Graph Factors 48
3.3.5 Hamilton Cycles of Planar Graphs 50
3.3.6 Self Avoiding Walks 53
3.3.7 Connectivity 55
4 Cook s versus Valiant s Hypothesis 61
4.1 Dependence on the Field 61
4.2 Statement of Main Results 64
4.3 Review of Discrete Complexity Classes 66
4.4 Relating NP to Counting Classes 68
4.5 A Bound on the Heights 70
4.6 Roots of Univariate Polynomials Modulo a Prime 75
4.7 Proof of Thm. 4.5 76
XII Contents
5 The Structure of Valiant s Complexity Classes 81
5.1 Outline and Comparison with Previous Work 81
5.2 An Abstract Diagonalization Theorem 82
5.3 An Abstract Embedding Theorem 85
5.4 Structure of Valiant s Complexity Classes 89
5.5 A Specific Family Neither Complete Nor p Computable .... 92
5.6 Relativized Complexity Classes 96
6 Fast Evaluation of Representations
of General Linear Groups 105
6.1 Description of the Problem 105
6.2 Preliminaries on Representations of GLTO 107
6.3 Auxiliary Fast Linear Algebra Algorithms 109
6.4 An Algorithm for Evaluating Representations 112
6.5 A Lower Bound 114
6.6 Fast Evaluation of Legendre Functions 115
7 The Complexity of Immanants 117
7.1 Motivation and Outline of Chapter 117
7.2 Fast Evaluation of Immanants 118
7.3 Completeness Results for Immanants 120
7.4 Character Formulas for the Symmetric Group 121
7.5 p Definability of Immanants 126
7.6 Completeness Proofs 128
8 Separation Results and Future Directions 135
8.1 Specific Families Which Are Not p Definable 135
8.2 Separations for the Complexity Class VQP 139
8.3 Possible Connections to Univariate Polynomials 141
8.4 Connections to the BSS Model 143
References 149
List of Notation 159
Index 163
|
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| discipline | Informatik Mathematik |
| format | Thesis Book |
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| indexdate | 2024-07-09T18:38:43Z |
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| isbn | 3540667520 |
| language | English |
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| series | Algorithms and computation in mathematics |
| series2 | Algorithms and computation in mathematics |
| spelling | Bürgisser, Peter 1962- Verfasser (DE-588)1041607911 aut Completeness and reduction in algebraic complexity theory Peter Bürgisser Berlin [u.a.] Springer 2000 XII, 168 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Algorithms and computation in mathematics 7 Zugl.: Zürich, Univ., Habil.-Schr. Computabilidade e complexidade larpcal Computational complexity Komplexitätstheorie (DE-588)4120591-1 gnd rswk-swf Berechnungskomplexität (DE-588)4134751-1 gnd rswk-swf Algebra (DE-588)4001156-2 gnd rswk-swf (DE-588)4113937-9 Hochschulschrift gnd-content Algebra (DE-588)4001156-2 s Komplexitätstheorie (DE-588)4120591-1 s DE-604 Berechnungskomplexität (DE-588)4134751-1 s Algorithms and computation in mathematics 7 (DE-604)BV011131286 7 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=008910420&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Bürgisser, Peter 1962- Completeness and reduction in algebraic complexity theory Algorithms and computation in mathematics Computabilidade e complexidade larpcal Computational complexity Komplexitätstheorie (DE-588)4120591-1 gnd Berechnungskomplexität (DE-588)4134751-1 gnd Algebra (DE-588)4001156-2 gnd |
| subject_GND | (DE-588)4120591-1 (DE-588)4134751-1 (DE-588)4001156-2 (DE-588)4113937-9 |
| title | Completeness and reduction in algebraic complexity theory |
| title_auth | Completeness and reduction in algebraic complexity theory |
| title_exact_search | Completeness and reduction in algebraic complexity theory |
| title_full | Completeness and reduction in algebraic complexity theory Peter Bürgisser |
| title_fullStr | Completeness and reduction in algebraic complexity theory Peter Bürgisser |
| title_full_unstemmed | Completeness and reduction in algebraic complexity theory Peter Bürgisser |
| title_short | Completeness and reduction in algebraic complexity theory |
| title_sort | completeness and reduction in algebraic complexity theory |
| topic | Computabilidade e complexidade larpcal Computational complexity Komplexitätstheorie (DE-588)4120591-1 gnd Berechnungskomplexität (DE-588)4134751-1 gnd Algebra (DE-588)4001156-2 gnd |
| topic_facet | Computabilidade e complexidade Computational complexity Komplexitätstheorie Berechnungskomplexität Algebra Hochschulschrift |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=008910420&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV011131286 |
| work_keys_str_mv | AT burgisserpeter completenessandreductioninalgebraiccomplexitytheory |