Introduction to circuit complexity: a uniform approach
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Berlin [u.a.]
Springer
1999
|
| Series: | Texts in theoretical computer science
|
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | XI, 270 S. |
| ISBN: | 3540643109 |
Staff View
MARC
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Record in the Search Index
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| adam_text | HERIBERT VOLLMER INTRODUCTION TO CIRCUIT COMPLEXITY A UNIFORM APPROACH
WITH 29 FIGURES SPRINGER TABLE OF CONTENTS INTRODUCTION 1 1. COMPLEXITY
MEASURES AND REDUCTIONS 5 1.1 AN EXAMPLE: ADDITION 5 1.2 CIRCUIT SIZE
AND DEPTH 7 1.3 MORE EXAMPLES 13 1.3.1 ITERATED ADDITION 13 1.3.2
MULTIPLICATION 16 1.3.3 MAJORITY 16 1.3.4 TRANSITIVE CLOSURE 16 1.4
CONSTANT-DEPTH REDUCTIONS 18 1.4.1 ITERATED ADDITION AND MULTIPLICATION
20 1.4.2 ITERATED MULTIPLICATION 21 1.4.3 COUNTING AND SORTING 24 1.5
ASYMPTOTIC COMPLEXITY 26 1.5.1 A LOWER BOUND 26 1.5.2 AN UPPER BOUND 28
BIBLIOGRAPHIC REMARKS 31 EXERCISES 32 2. RELATIONS TO OTHER COMPUTATION
MODELS 35 2.1 TIME ON TURING MACHINES 36 2.2 SPACE ON TURING MACHINES 41
2.3 NON-UNIFORM TURING MACHINES 42 2.4 UNIFORM CIRCUIT FAMILIES 46 2.5
ALTERNATING TURING MACHINES 53 2.5.1 COMPUTATION MODEL AND COMPLEXITY
MEASURES 53 2.5.2 RELATIONS TO DETERMINISTIC COMPLEXITY 56 2.5.3 AN
EXAMPLE: ADDITION 57 2.5.4 INPUT NORMAL FORM 58 2.6 SIMULTANEOUS
RESOURCE BOUNDS 60 2.6.1 UNIFORMITY 60 2.6.2 TIME AND SPACE ON
ALTERNATING MACHINES 63 2.7 PARALLEL RANDOM ACCESS MACHINES 67 TABLE OF
CONTENTS BIBLIOGRAPHIC REMARKS 74 EXERCISES 75 3. LOWER BOUNDS 79 3.1
THE ELIMINATION METHOD 80 3.1.1 A LOWER BOUND FOR THE THRESHOLD FUNCTION
80 3.1.2 A LOWER BOUND FOR THE PARITY FUNCTION 81 3.2 THE POLYNOMIAL
METHOD , 84 3.2.1 PERCEPTRONS AND POLYNOMIAL REPRESENTATIONS 84 3.2.2
DEGREE LOWER BOUNDS 86 3.3 LOWER BOUNDS FOR CONSTANT-DEPTH CIRCUITS 89
3.3.1 DEPTH REDUCTION FOR CONSTANT-DEPTH CIRCUITS 89 3.3.2 APPROXIMATING
CIRCUITS BY POLYNOMIALS 95 3.3.3 SMOLENSKY S THEOREM 96 BIBLIOGRAPHIC
REMARKS 102 EXERCISES 104 4. THE NC HIERARCHY 107 4.1 BOUNDED FAN-IN
CIRCUITS 107 4.2 UNBOUNDED FAN-IN CIRCUITS 108 4.3 SEMI-UNBOUNDED FAN-IN
CIRCUITS 110 4.3.1 POLYNOMIAL TREE-SIZE ILL 4.3.2 CLOSURE UNDER
COMPLEMENTATION 113 4.4 THE DECOMPOSABILITY OF THE NC HIERARCHY 118 4.5
CLASSES WITHIN NC 1 122 4.5.1 UNIFORMITY WITHIN NC 1 122 4.5.2 A
HIERARCHY OF CLASSES WITHIN NC 1 126 4.5.3 ALGEBRAIC CHARACTERIZATIONS
127 4.5.4 A LOGICAL CHARACTERIZATION 136 4.6 P-COMPLETENESS 149 4.6.1
REDUCIBILITY NOTIONS 149 4.6.2 CIRCUIT VALUE PROBLEMS 152 4.6.3 GRAPH
PROBLEMS 154 4.6.4 PROBLEMS FROM LOGIC, ALGEBRA, AND LANGUAGE THEORY .
156 4.7 OVERVIEW OF THE CLASSES OF THE NC HIERARCHY 159 BIBLIOGRAPHIC
REMARKS 160 EXERCISES 164 5. ARITHMETIC CIRCUITS 173 5.1 COMPLEXITY
MEASURES AND REDUCTIONS 173 5.2 EVALUATING ARITHMETIC CIRCUITS BY
STRAIGHT-LINE PROGRAMS ... 178 5.3 COUNTING PROBLEMS IN BOOLEAN CIRCUITS
181 5.3.1 COUNTING IN SAC 1 184 5.3.2 COUNTING IN NC 1 190 5.3.3
COUNTING IN AC 0 199 TABLE OF CONTENTS XI 5.4 RELATIONS AMONG ARITHMETIC
AND BOOLEAN CIRCUIT CLASSES .... 206 BIBLIOGRAPHIC REMARKS 208 EXERCISES
210 6. POLYNOMIAL TIME AND BEYOND 215 6.1 THE CLASS P/POLY 215 6.1.1 BPP
AND P/POLY 216 6.1.2 NP AND P/POLY 217 6.1.3 LOWER BOUNDS FOR P/POLY 220
6.1.4 LOWER BOUNDS FOR UNIFORM CIRCUITS 222 6.2 A LOWER BOUND FOR
UNIFORM THRESHOLD CIRCUITS 223 BIBLIOGRAPHIC REMARKS 228 EXERCISES 229
APPENDIX: MATHEMATICAL PRELIMINARIES 233 AL ALPHABETS, WORDS, LANGUAGES
233 A2 BINARY ENCODING 233 A3 ASYMPTOTIC BEHAVIOR OF FUNCTIONS 234 A4
TURING MACHINES 234 A5 LOGIC 236 A6 GRAPHS 237 A7 NUMBERS AND FUNCTIONS
237 A8 ALGEBRAIC STRUCTURES 239 A9 LINEAR ALGEBRA 239 BIBLIOGRAPHY 241
LIST OF FIGURES 255 AUTHOR INDEX 257 SUBJECT INDEX 261
|
| any_adam_object | 1 |
| author | Vollmer, Heribert 1964- |
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| author_role | aut |
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| author_variant | h v hv |
| building | Verbundindex |
| bvnumber | BV012596091 |
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| dewey-full | 005.131 |
| dewey-hundreds | 000 - Computer science, information, general works |
| dewey-ones | 005 - Computer programming, programs, data, security |
| dewey-raw | 005.131 |
| dewey-search | 005.131 |
| dewey-sort | 15.131 |
| dewey-tens | 000 - Computer science, information, general works |
| discipline | Informatik |
| format | Book |
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| illustrated | Not Illustrated |
| indexdate | 2024-07-09T18:30:18Z |
| institution | BVB |
| isbn | 3540643109 |
| language | English |
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| physical | XI, 270 S. |
| publishDate | 1999 |
| publishDateSearch | 1999 |
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| publisher | Springer |
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| series2 | Texts in theoretical computer science |
| spelling | Vollmer, Heribert 1964- Verfasser (DE-588)121026027 aut Introduction to circuit complexity a uniform approach Heribert Vollmer Berlin [u.a.] Springer 1999 XI, 270 S. txt rdacontent n rdamedia nc rdacarrier Texts in theoretical computer science Boole, Algèbre de ram Complexité de calcul (informatique) ram Logique symbolique et mathématique ram Ordinateurs - Circuits ram circuit booléen inriac circuit commutation inriac complexité circuit inriac Boolesche Funktion (DE-588)4146281-6 gnd rswk-swf Berechnungskomplexität (DE-588)4134751-1 gnd rswk-swf Boolesche Funktion (DE-588)4146281-6 s Berechnungskomplexität (DE-588)4134751-1 s DE-604 HEBIS Datenaustausch Darmstadt application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=008554095&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Vollmer, Heribert 1964- Introduction to circuit complexity a uniform approach Boole, Algèbre de ram Complexité de calcul (informatique) ram Logique symbolique et mathématique ram Ordinateurs - Circuits ram circuit booléen inriac circuit commutation inriac complexité circuit inriac Boolesche Funktion (DE-588)4146281-6 gnd Berechnungskomplexität (DE-588)4134751-1 gnd |
| subject_GND | (DE-588)4146281-6 (DE-588)4134751-1 |
| title | Introduction to circuit complexity a uniform approach |
| title_auth | Introduction to circuit complexity a uniform approach |
| title_exact_search | Introduction to circuit complexity a uniform approach |
| title_full | Introduction to circuit complexity a uniform approach Heribert Vollmer |
| title_fullStr | Introduction to circuit complexity a uniform approach Heribert Vollmer |
| title_full_unstemmed | Introduction to circuit complexity a uniform approach Heribert Vollmer |
| title_short | Introduction to circuit complexity |
| title_sort | introduction to circuit complexity a uniform approach |
| title_sub | a uniform approach |
| topic | Boole, Algèbre de ram Complexité de calcul (informatique) ram Logique symbolique et mathématique ram Ordinateurs - Circuits ram circuit booléen inriac circuit commutation inriac complexité circuit inriac Boolesche Funktion (DE-588)4146281-6 gnd Berechnungskomplexität (DE-588)4134751-1 gnd |
| topic_facet | Boole, Algèbre de Complexité de calcul (informatique) Logique symbolique et mathématique Ordinateurs - Circuits circuit booléen circuit commutation complexité circuit Boolesche Funktion Berechnungskomplexität |
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