Proclaiming dictators and juntas or testing boolean formulae

Michal Parnas; Dana Ron; Alex Samorodnitsky

doi:10.1007/3-540-44666-4_30

Proclaiming dictators and juntas or testing boolean formulae

Michal Parnas, Dana Ron, Alex Samorodnitsky

School of Electrical Engineering

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

Abstract

We consider the problem of determining whether a given function f: {0, 1}ⁿ → {0, 1} belongs to a certain class of Boolean functions F or whether it is far from the class. More precisely, given query access to the function f and given a distance parameter ϵ, we wou ld like to decide whether f∈F or whether it differs from every g ∈F on more than an ϵ -fraction of the domain elements. The classes of functions we consider are singleton (“dictatorship”) functions, monomials, and monotone DNF functions with a bounded number of terms. In all cases we provide algorithms whose query complexity is independent of n (the number of function variables), and polynomial in the other relevant parameters.

Original language	English
Title of host publication	Approximation, Randomization, and Combinatorial Optimization
Subtitle of host publication	Algorithms and Techniques - 4th International Workshop on Approximation, Algorithms for Combinatorial Optimization Problems, APPROX 2001 and 5th International Workshop on Randomization and Approximation Techniques in Computer Science, RANDOM 2001, Proceedings
Editors	Michel Goemans, Klaus Jansen, Jose D. P. Rolim, Luca Trevisan
Place of Publication	Berlin Heidelberg
Publisher	Springer Verlag
Pages	273-285
Number of pages	13
ISBN (Electronic)	3540424709, 78-3-540-44666-8
ISBN (Print)	978-3-540-42470-3
DOIs	https://doi.org/10.1007/3-540-44666-4_30
State	Published - 2001
Event	4th International Workshop on Approximation Algorithms for Combinatorial Optimization Problems, APPROX 2001 and 5th International Workshop on Randomization and Approximation Techniques in Computer Science, RANDOM 2001 - Berkeley, United States Duration: 18 Aug 2001 → 20 Aug 2001

Publication series

Name	Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume	2129
ISSN (Print)	0302-9743
ISSN (Electronic)	1611-3349

Conference

Conference	4th International Workshop on Approximation Algorithms for Combinatorial Optimization Problems, APPROX 2001 and 5th International Workshop on Randomization and Approximation Techniques in Computer Science, RANDOM 2001
Country/Territory	United States
City	Berkeley
Period	18/08/01 → 20/08/01

Keywords

Learning algorithms
boolean function
parity function
query complexity
testing algorithm

Access to Document

10.1007/3-540-44666-4_30

Cite this

Parnas, M., Ron, D., & Samorodnitsky, A. (2001). Proclaiming dictators and juntas or testing boolean formulae. In M. Goemans, K. Jansen, J. D. P. Rolim, & L. Trevisan (Eds.), Approximation, Randomization, and Combinatorial Optimization: Algorithms and Techniques - 4th International Workshop on Approximation, Algorithms for Combinatorial Optimization Problems, APPROX 2001 and 5th International Workshop on Randomization and Approximation Techniques in Computer Science, RANDOM 2001, Proceedings (pp. 273-285). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 2129). Springer Verlag. https://doi.org/10.1007/3-540-44666-4_30

Parnas, Michal ; Ron, Dana ; Samorodnitsky, Alex. / Proclaiming dictators and juntas or testing boolean formulae. Approximation, Randomization, and Combinatorial Optimization: Algorithms and Techniques - 4th International Workshop on Approximation, Algorithms for Combinatorial Optimization Problems, APPROX 2001 and 5th International Workshop on Randomization and Approximation Techniques in Computer Science, RANDOM 2001, Proceedings. editor / Michel Goemans ; Klaus Jansen ; Jose D. P. Rolim ; Luca Trevisan. Berlin Heidelberg : Springer Verlag, 2001. pp. 273-285 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)).

@inproceedings{32f693e5ff6a48f2b0acabf3aa1e63b9,

title = "Proclaiming dictators and juntas or testing boolean formulae",

abstract = "We consider the problem of determining whether a given function f: {0, 1}n → {0, 1} belongs to a certain class of Boolean functions F or whether it is far from the class. More precisely, given query access to the function f and given a distance parameter ϵ, we wou ld like to decide whether f∈F or whether it differs from every g ∈F on more than an ϵ -fraction of the domain elements. The classes of functions we consider are singleton (“dictatorship”) functions, monomials, and monotone DNF functions with a bounded number of terms. In all cases we provide algorithms whose query complexity is independent of n (the number of function variables), and polynomial in the other relevant parameters.",

keywords = "Learning algorithms, boolean function, parity function, query complexity, testing algorithm",

author = "Michal Parnas and Dana Ron and Alex Samorodnitsky",

note = "Publisher Copyright: {\textcopyright} Springer-Verlag Berlin Heidelberg 2001; 4th International Workshop on Approximation Algorithms for Combinatorial Optimization Problems, APPROX 2001 and 5th International Workshop on Randomization and Approximation Techniques in Computer Science, RANDOM 2001 ; Conference date: 18-08-2001 Through 20-08-2001",

year = "2001",

doi = "10.1007/3-540-44666-4_30",

language = "אנגלית",

isbn = "978-3-540-42470-3",

series = "Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)",

publisher = "Springer Verlag",

pages = "273--285",

editor = "Michel Goemans and Klaus Jansen and Rolim, {Jose D. P.} and Luca Trevisan",

booktitle = "Approximation, Randomization, and Combinatorial Optimization",

}

Parnas, M, Ron, D & Samorodnitsky, A 2001, Proclaiming dictators and juntas or testing boolean formulae. in M Goemans, K Jansen, JDP Rolim & L Trevisan (eds), Approximation, Randomization, and Combinatorial Optimization: Algorithms and Techniques - 4th International Workshop on Approximation, Algorithms for Combinatorial Optimization Problems, APPROX 2001 and 5th International Workshop on Randomization and Approximation Techniques in Computer Science, RANDOM 2001, Proceedings. Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), vol. 2129, Springer Verlag, Berlin Heidelberg, pp. 273-285, 4th International Workshop on Approximation Algorithms for Combinatorial Optimization Problems, APPROX 2001 and 5th International Workshop on Randomization and Approximation Techniques in Computer Science, RANDOM 2001, Berkeley, United States, 18/08/01. https://doi.org/10.1007/3-540-44666-4_30

Proclaiming dictators and juntas or testing boolean formulae. / Parnas, Michal; Ron, Dana; Samorodnitsky, Alex.
Approximation, Randomization, and Combinatorial Optimization: Algorithms and Techniques - 4th International Workshop on Approximation, Algorithms for Combinatorial Optimization Problems, APPROX 2001 and 5th International Workshop on Randomization and Approximation Techniques in Computer Science, RANDOM 2001, Proceedings. ed. / Michel Goemans; Klaus Jansen; Jose D. P. Rolim; Luca Trevisan. Berlin Heidelberg: Springer Verlag, 2001. p. 273-285 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 2129).

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

TY - GEN

T1 - Proclaiming dictators and juntas or testing boolean formulae

AU - Parnas, Michal

AU - Ron, Dana

AU - Samorodnitsky, Alex

N1 - Publisher Copyright: © Springer-Verlag Berlin Heidelberg 2001

PY - 2001

Y1 - 2001

N2 - We consider the problem of determining whether a given function f: {0, 1}n → {0, 1} belongs to a certain class of Boolean functions F or whether it is far from the class. More precisely, given query access to the function f and given a distance parameter ϵ, we wou ld like to decide whether f∈F or whether it differs from every g ∈F on more than an ϵ -fraction of the domain elements. The classes of functions we consider are singleton (“dictatorship”) functions, monomials, and monotone DNF functions with a bounded number of terms. In all cases we provide algorithms whose query complexity is independent of n (the number of function variables), and polynomial in the other relevant parameters.

AB - We consider the problem of determining whether a given function f: {0, 1}n → {0, 1} belongs to a certain class of Boolean functions F or whether it is far from the class. More precisely, given query access to the function f and given a distance parameter ϵ, we wou ld like to decide whether f∈F or whether it differs from every g ∈F on more than an ϵ -fraction of the domain elements. The classes of functions we consider are singleton (“dictatorship”) functions, monomials, and monotone DNF functions with a bounded number of terms. In all cases we provide algorithms whose query complexity is independent of n (the number of function variables), and polynomial in the other relevant parameters.

KW - Learning algorithms

KW - boolean function

KW - parity function

KW - query complexity

KW - testing algorithm

UR - http://www.scopus.com/inward/record.url?scp=84923114993&partnerID=8YFLogxK

U2 - 10.1007/3-540-44666-4_30

DO - 10.1007/3-540-44666-4_30

M3 - ???researchoutput.researchoutputtypes.contributiontobookanthology.conference???

AN - SCOPUS:84923114993

SN - 978-3-540-42470-3

T3 - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

SP - 273

EP - 285

BT - Approximation, Randomization, and Combinatorial Optimization

A2 - Goemans, Michel

A2 - Jansen, Klaus

A2 - Rolim, Jose D. P.

A2 - Trevisan, Luca

PB - Springer Verlag

CY - Berlin Heidelberg

T2 - 4th International Workshop on Approximation Algorithms for Combinatorial Optimization Problems, APPROX 2001 and 5th International Workshop on Randomization and Approximation Techniques in Computer Science, RANDOM 2001

Y2 - 18 August 2001 through 20 August 2001

ER -

Parnas M, Ron D, Samorodnitsky A. Proclaiming dictators and juntas or testing boolean formulae. In Goemans M, Jansen K, Rolim JDP, Trevisan L, editors, Approximation, Randomization, and Combinatorial Optimization: Algorithms and Techniques - 4th International Workshop on Approximation, Algorithms for Combinatorial Optimization Problems, APPROX 2001 and 5th International Workshop on Randomization and Approximation Techniques in Computer Science, RANDOM 2001, Proceedings. Berlin Heidelberg: Springer Verlag. 2001. p. 273-285. (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)). doi: 10.1007/3-540-44666-4_30

Proclaiming dictators and juntas or testing boolean formulae

Abstract

Publication series

Conference

Keywords

Access to Document

Other files and links

Fingerprint

Cite this