On the average sensitivity of testing square-free numbers
Identifieur interne :
001787 ( PascalFrancis/Curation );
précédent :
001786;
suivant :
001788
On the average sensitivity of testing square-free numbers
Auteurs : A. Bernasconi [
Allemagne] ;
C. Damm [
Allemagne] ;
I. E. Shparlinski [
Australie]
Source :
-
Lecture notes in computer science [ 0302-9743 ] ; 1999.
RBID : Pascal:99-0419773
Descripteurs français
English descriptors
Abstract
We study combinatorial complexity characteristics of a Boolean function related to a natural number theoretic problem. In particular we obtain a linear lower bound on the average sensitivity of the Boolean function deciding whether a given integer is square-free. This result allows us to derive a quadratic lower bound for the formula size complexity of testing square-free numbers and a linear lower bound on the average decision tree depth. We also obtain lower bounds on the degrees of exact and approximative polynomial representations of this function.
| pA |
| A01 | 01 | 1 | | @0 0302-9743 |
|---|
| A05 | | | | @2 1627 |
|---|
| A08 | 01 | 1 | ENG | @1 On the average sensitivity of testing square-free numbers |
|---|
| A09 | 01 | 1 | ENG | @1 COCOON '99 : computing and combinatorics : Tokyo, 26-28 July 1999 |
|---|
| A11 | 01 | 1 | | @1 BERNASCONI (A.) |
|---|
| A11 | 02 | 1 | | @1 DAMM (C.) |
|---|
| A11 | 03 | 1 | | @1 SHPARLINSKI (I. E.) |
|---|
| A12 | 01 | 1 | | @1 ASANO (Takao) @9 ed. |
|---|
| A12 | 02 | 1 | | @1 IMAI (Hiroshi) @9 ed. |
|---|
| A12 | 03 | 1 | | @1 LEE (D.T.) @9 ed. |
|---|
| A12 | 04 | 1 | | @1 NAKANO (Shin-Ichi) @9 ed. |
|---|
| A12 | 05 | 1 | | @1 TOKUYAMA (Takeshi) @9 ed. |
|---|
| A14 | 01 | | | @1 Institut für Informatik, Technische Universität München @2 80290 München @3 DEU @Z 1 aut. |
|---|
| A14 | 02 | | | @1 Fachbereich für Informatik, Universität Trier @2 54286 Trier @3 DEU @Z 2 aut. |
|---|
| A14 | 03 | | | @1 School of MPCE, Macquarie University @2 Sydney, NSW 2109 @3 AUS @Z 3 aut. |
|---|
| A20 | | | | @1 291-299 |
|---|
| A21 | | | | @1 1999 |
|---|
| A23 | 01 | | | @0 ENG |
|---|
| A26 | 01 | | | @0 3-540-66200-6 |
|---|
| A43 | 01 | | | @1 INIST @2 16343 @5 354000084544990290 |
|---|
| A44 | | | | @0 0000 @1 © 1999 INIST-CNRS. All rights reserved. |
|---|
| A45 | | | | @0 19 ref. |
|---|
| A47 | 01 | 1 | | @0 99-0419773 |
|---|
| A60 | | | | @1 P @2 C |
|---|
| A61 | | | | @0 A |
|---|
| A64 | 01 | 1 | | @0 Lecture notes in computer science |
|---|
| A66 | 01 | | | @0 DEU |
|---|
| A66 | 02 | | | @0 USA |
|---|
| C01 | 01 | | ENG | @0 We study combinatorial complexity characteristics of a Boolean function related to a natural number theoretic problem. In particular we obtain a linear lower bound on the average sensitivity of the Boolean function deciding whether a given integer is square-free. This result allows us to derive a quadratic lower bound for the formula size complexity of testing square-free numbers and a linear lower bound on the average decision tree depth. We also obtain lower bounds on the degrees of exact and approximative polynomial representations of this function. |
|---|
| C02 | 01 | X | | @0 001D02A06 |
|---|
| C03 | 01 | X | FRE | @0 Informatique théorique @5 01 |
|---|
| C03 | 01 | X | ENG | @0 Computer theory @5 01 |
|---|
| C03 | 01 | X | SPA | @0 Informática teórica @5 01 |
|---|
| C03 | 02 | 3 | FRE | @0 Complexité communication @5 02 |
|---|
| C03 | 02 | 3 | ENG | @0 Communication complexity @5 02 |
|---|
| C03 | 03 | X | FRE | @0 Circuit combinatoire @5 03 |
|---|
| C03 | 03 | X | ENG | @0 Combinatory circuit @5 03 |
|---|
| C03 | 03 | X | SPA | @0 Circuito combinatorio @5 03 |
|---|
| C03 | 04 | X | FRE | @0 Fonction booléenne @5 04 |
|---|
| C03 | 04 | X | ENG | @0 Boolean function @5 04 |
|---|
| C03 | 04 | X | SPA | @0 Función booliana @5 04 |
|---|
| C03 | 05 | X | FRE | @0 Classe complexité @5 05 |
|---|
| C03 | 05 | X | ENG | @0 Complexity class @5 05 |
|---|
| C03 | 05 | X | SPA | @0 Clase complejidad @5 05 |
|---|
| N21 | | | | @1 270 |
|---|
|
|---|
| pR |
| A30 | 01 | 1 | ENG | @1 Computing and combinatorics. Annual international conference @2 5 @3 Tokyo JPN @4 1999-07-26 |
|---|
|
|---|
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Le document en format XML
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</keywords><front><div type="abstract" xml:lang="en">We study combinatorial complexity characteristics of a Boolean function related to a natural number theoretic problem. In particular we obtain a linear lower bound on the average sensitivity of the Boolean function deciding whether a given integer is square-free. This result allows us to derive a quadratic lower bound for the formula size complexity of testing square-free numbers and a linear lower bound on the average decision tree depth. We also obtain lower bounds on the degrees of exact and approximative polynomial representations of this function.</div>
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