Boolean functions and computation models:
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Berlin [u.a.]
Springer
2002
|
| Series: | Texts in theoretical computer science
|
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | XIV, 601 S. graph. Darst. |
| ISBN: | 3540594361 |
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| adam_text | PETER CLOTE * EVANGELOS KRANAKIS BOOLEAN FUNCTIONS AND COMPUTATION
MODELS WITH 19 FIGURES SPRINGER * CONTENTS 1. BOOLEAN FUNCTIONS AND
CIRCUITS 1 1.1 INTRODUCTION 1 1.2 BOOLEAN FUNCTIONS AND FORMULAS 2 1.3
CIRCUIT MODEL 7 1.4 BASIC FUNCTIONS AND REDUCTIONS 8 1.5 NOMENCLATURE 11
1.6 PARSING REGULAR AND CONTEXT-FREE LANGUAGES 12 1.7 CIRCUITS FOR
INTEGER ARITHMETIC 17 1.7.1 CIRCUITS FOR ADDITION AND MULTIPLICATION 17
1.7.2 DIVISION USING NEWTON ITERATION 21 1.7.3 DIVISION USING ITERATED
PRODUCT 24 1.8 SYNTHESIS OF CIRCUITS 30 1.8.1 ELEMENTARY METHODS 30
1.8.2 SHANNON S METHOD 31 1.8.3 LUPANOV S METHOD 32 1.8.4 SYMMETRIC
FUNCTIONS 34 1.9 REDUCING THE FAN-OUT 35 1.10 RELATING FORMULA SIZE AND
DEPTH 39 1.11 OTHER MODELS 45 1.11.1 SWITCHING NETWORKS 45 1.11.2 VLSI
CIRCUITS 45 1.11.3 ENERGY CONSUMPTION 45 1.11.4 BOOLEAN CELLULAR
AUTOMATA 46 1.11.5 BRANCHING PROGRAMS 48 1.11.6 HOPFIELD NETS 53 1.11.7
COMMUNICATION COMPLEXITY 54 1.11.8 ANONYMOUS NETWORKS 54 1.12 HISTORICAL
AND BIBLIOGRAPHICAL REMARKS 55 1.13 EXERCISES 56 2. CIRCUIT LOWER BOUNDS
61 2.1 INTRODUCTION 61 2.2 SHANNON S LOWER BOUND 63 2.3 NECHIPORUK S
BOUND 65 XII CONTENTS 2.4 MONOTONIC REAL CIRCUITS 68 2.4.1 BROKEN
MOSQUITO SCREEN 68 2.4.2 MONOTONIC REAL CIRCUITS ARE POWERFUL 77 2.4.3
SI-CONNECTIVITY 78 2.5 PARITY AND THE RANDOM RESTRICTION METHOD 90 2.6
PROBABILISTIC METHODS 95 2.6.1 HASTAD S LOWER BOUND FOR PARITY 96 2.6.2
DEPTH-/C VERSUS DEPTH-(FC - 1) 99 2.6.3 RAZBOROV S SIMPLIFICATION AND
DECISION TREES 102 2.6.4 A HYBRID SWITCHING LEMMA AND SI-CONNECTIVITY
107 2.6.5 HYBRID SWITCHING WITH THE UNIFORM DISTRIBUTION 110 2.7
ALGEBRAIC METHODS 124 2.7.1 RAZBOROV S LOWER BOUND FOR MAJORITY OVER
BOOLEAN CIRCUITS WITH PARITY 124 2.7.2 SMOLENSKY S LOWER BOUND FOR MOD P
VERSUS MOD ? .... 129 2.8 POLYNOMIAL METHOD 132 2.8.1 ON THE STRENGTH OF
MOD M GATES 132 2.8.2 THE MOD M -DEGREE OF THRESHOLD FUNCTIONS 135 2.9
METHOD OF FILTERS 137 2.10 ELIMINATING MAJORITY GATES 140 2.11 CIRCUITS
FOR SYMMETRIC FUNCTIONS 141 2.11.1 NEGATIVE RESULTS 143 2.11.2 POSITIVE
RESULTS 145 2.12 PROBABILISTIC CIRCUITS 146 2.13 HISTORICAL AND
BIBLIOGRAPHICAL REMARKS 148 2.14 EXERCISES 150 3. CIRCUIT UPPER BOUNDS
155 3.1 INTRODUCTION 155 3.2 DEFINITIONS AND ELEMENTARY PROPERTIES 156
3.3 POLYA S ENUMERATION THEORY 162 3.4 REPRESENTABILITY OF PERMUTATION
GROUPS 164 3.5 ALGORITHM FOR REPRESENTING CYCLIC GROUPS 168 3.6
ASYMPTOTICS FOR INVARIANCE GROUPS 172 3.7 ALMOST SYMMETRIC LANGUAGES 174
3.8 SYMMETRY AND COMPLEXITY 178 3.9 APPLICATIONS TO ANONYMOUS NETWORKS
184 3.9.1 RINGS 185 3.9.2 HYPERCUBES 185 3.10 HISTORICAL AND
BIBLIOGRAPHICAL REMARKS 194 3.11 EXERCISES 194 4. RANDOMNESS AND
SATISFIABILITY 207 4.1 INTRODUCTION * 207 4.2 THRESHOLD FOR 2-SAT 209
CONTENTS XIII 4.3 UNSATISFIABILITY THRESHOLD FOR 3-SAT 212 4.3.1 A
GENERAL METHOD AND LOCAL MAXIMA 213 4.3.2 METHOD OF SINGLE FLIPS 214
4.3.3 APPROXIMATING THE THRESHOLD 217 4.3.4 METHOD OF DOUBLE FLIPS 217
4.3.5 PROBABILITY CALCULATIONS 218 4.4 SATISFIABILITY THRESHOLD FOR
3-SAT 224 4.4.1 SATISFIABILITY HEURISTICS 224 4.4.2 THRESHOLD 226 4.5 (2
+ P)-SAT 229 4.5.1 UNSATISFIABILITY THRESHOLD 230 4.5.2 TRANSITION FROM
2-SAT TO 3-SAT 232 4.6 CONSTRAINT PROGRAMMING 235 4.6.1 MODELS OF CSP
236 4.6.2 A NEW MODEL FOR RANDOM CSP 238 4.6.3 THE METHOD OF LOCAL
MAXIMA 239 4.6.4 THRESHOLD FOR MODEL E 241 4.7 HISTORICAL AND
BIBLIOGRAPHICAL REMARKS 242 4.8 EXERCISES 243 5. PROPOSITIONAL PROOF
SYSTEMS 247 5.1 INTRODUCTION 247 5.2 COMPLEXITY OF PROOFS 249 5.3
GENTZEN SEQUENT CALCULUS LK 255 5.3.1 COMPLETENESS 257 5.3.2 LOWER BOUND
FOR CUT-FREE GENTZEN 259 5.3.3 MONOTONIC SEQUENT CALCULUS 267 5.4
RESOLUTION 268 5.4.1 RESOLUTION AND THE PHP . . . : 271 5.4.2 RESOLUTION
AND ODD-CHARGED GRAPHS 279 5.4.3 SCHONING S EXPANDER GRAPHS AND
RESOLUTION 285 5.4.4 WIDTH-BOUNDED RESOLUTION PROOFS 291 5.4.5
INTERPOLATION AND SI-CONNECTIVITY 296 5.4.6 PHASE TRANSITION AND LENGTH
OF RESOLUTION PROOFS .... 300 5.5 ALGEBRAIC REFUTATION SYSTEMS 306 5.5.1
NULLSTELLENSATZ 308 5.5.2 POLYNOMIAL CALCULUS . 316 5.5.3 GAUSSIAN
CALCULUS 324 5.5.4 BINOMIAL CALCULUS 326 5.5.5 LOWER BOUNDS FOR THE
POLYNOMIAL CALCULUS 332 5.5.6 RANDOM CNF FORMULAS AND THE POLYNOMIAL
CALCULUS . . 337 5.6 CUTTING PLANES CP 343 5.6.1 COMPLETENESS OF CP 345
5.6.2 CUTTING PLANES AND THE PHP 348 5.6.3 POLYNOMIAL EQUIVALENCE OF CP2
AND CP 353 XIV CONTENTS 5.6.4 NORMAL FORM FOR CP PROOFS 355 5.6.5 LOWER
BOUNDS FOR CP 359 5.6.6 THRESHOLD LOGIC PTK 366 5.7 FREGE SYSTEMS 370
5.7.1 BOUNDED DEPTH FREGE SYSTEMS 372 5.7.2 EXTENDED FREGE SYSTEMS 393
5.7.3 FREGE SYSTEMS AND THE PHP 398 5.8 OPEN PROBLEMS 403 5.9 HISTORICAL
AND BIBLIOGRAPHICAL REMARKS 405 5.10 EXERCISES 406 6. MACHINE MODELS AND
FUNCTION ALGEBRAS 413 6.1 INTRODUCTION 413 6.2 MACHINE MODELS 415 6.2.1
TURING MACHINES 415 6.2.2 PARALLEL MACHINE MODEL 424 6.2.3 EXAMPLE
PARALLEL ALGORITHMS 427 6.2.4 LOGP MODEL 433 6.2.5 CIRCUIT FAMILIES : .
434 6.3 SOME RECURSION SCHEMES 437 6.3.1 AN ALGEBRA FOR THE LOGTIME
HIERARCHY LH 438 6.3.2 BOUNDED RECURSION ON NOTATION 450 6.3.3 BOUNDED
RECURSION 458 6.3.4 BOUNDED MINIMIZATION 465 6.3.5 MISCELLANEOUS 470
6.3.6 SAFE RECURSION 478 6.4 A GLIMPSE OF OTHER WORK 487 6.5 HISTORICAL
AND BIBLIOGRAPHICAL REMARKS 488 6.6 EXERCISES 489 7. HIGHER TYPES 497
7.1 INTRODUCTION 497 7.2 TYPE 2 FUNCTIONAL 497 7.3 SOME CLOSURE
PROPERTIES OF AQ 502 7.4 SQUARE-ROOT AND MULTIPLE RECURSION 511 7.5
PARALLEL MACHINE MODEL 527 7.6 A-CALCULI FOR PARALLEL COMPUTABLE HIGHER
TYPE FUNCTIONALS . . 554 7.6.1 INTRODUCTION TO HIGHER TYPES 555 7.6.2
P-TYPES 556 7.6.3 FINITE TYPED LAMBDA CALCULUS 558 7.7 HISTORICAL AND
BIBLIOGRAPHICAL REMARKS 564 7.8 EXERCISES 565 REFERENCES 569 INDEX 591
|
| any_adam_object | 1 |
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| dewey-hundreds | 500 - Natural sciences and mathematics |
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| dewey-search | 511.3 |
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| dewey-tens | 510 - Mathematics |
| discipline | Informatik Mathematik |
| format | Book |
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| illustrated | Illustrated |
| indexdate | 2024-07-09T18:51:08Z |
| institution | BVB |
| isbn | 3540594361 |
| language | English |
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| spelling | Clote, Peter Verfasser aut Boolean functions and computation models Peter Clote ; Evangelos Kranakis Berlin [u.a.] Springer 2002 XIV, 601 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Texts in theoretical computer science Algoritmen gtt Boole, Algèbre de Boolean-functions gtt Complexité de calcul (Informatique) Algebra, Boolean Computational complexity Boolesche Funktion (DE-588)4146281-6 gnd rswk-swf Mathematisches Modell (DE-588)4114528-8 gnd rswk-swf Computer (DE-588)4070083-5 gnd rswk-swf Berechnungskomplexität (DE-588)4134751-1 gnd rswk-swf Computer (DE-588)4070083-5 s Mathematisches Modell (DE-588)4114528-8 s DE-604 Boolesche Funktion (DE-588)4146281-6 s Berechnungskomplexität (DE-588)4134751-1 s Kranakis, Evangelos Verfasser aut HEBIS Datenaustausch Darmstadt application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=009390946&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Clote, Peter Kranakis, Evangelos Boolean functions and computation models Algoritmen gtt Boole, Algèbre de Boolean-functions gtt Complexité de calcul (Informatique) Algebra, Boolean Computational complexity Boolesche Funktion (DE-588)4146281-6 gnd Mathematisches Modell (DE-588)4114528-8 gnd Computer (DE-588)4070083-5 gnd Berechnungskomplexität (DE-588)4134751-1 gnd |
| subject_GND | (DE-588)4146281-6 (DE-588)4114528-8 (DE-588)4070083-5 (DE-588)4134751-1 |
| title | Boolean functions and computation models |
| title_auth | Boolean functions and computation models |
| title_exact_search | Boolean functions and computation models |
| title_full | Boolean functions and computation models Peter Clote ; Evangelos Kranakis |
| title_fullStr | Boolean functions and computation models Peter Clote ; Evangelos Kranakis |
| title_full_unstemmed | Boolean functions and computation models Peter Clote ; Evangelos Kranakis |
| title_short | Boolean functions and computation models |
| title_sort | boolean functions and computation models |
| topic | Algoritmen gtt Boole, Algèbre de Boolean-functions gtt Complexité de calcul (Informatique) Algebra, Boolean Computational complexity Boolesche Funktion (DE-588)4146281-6 gnd Mathematisches Modell (DE-588)4114528-8 gnd Computer (DE-588)4070083-5 gnd Berechnungskomplexität (DE-588)4134751-1 gnd |
| topic_facet | Algoritmen Boole, Algèbre de Boolean-functions Complexité de calcul (Informatique) Algebra, Boolean Computational complexity Boolesche Funktion Mathematisches Modell Computer Berechnungskomplexität |
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