Proclaiming dictators and juntas or testing boolean formulae

Michal Parnas; Dana Ron; Alex Samorodnitsky

Proclaiming dictators and juntas or testing boolean formulae

Michal Parnas, Dana Ron, Alex Samorodnitsky

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

2 Scopus citations

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	Luca Trevisan, Klaus Jansen, Michel Goemans, Jose D. P. Rolim
Publisher	Springer Verlag
Pages	273-285
Number of pages	13
ISBN (Electronic)	3540424709
State	Published - 2015
Externally published	Yes
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

Bibliographical note

Publisher Copyright:
© Springer-Verlag Berlin Heidelberg 2001

Funding

Funders	Funder number
Israel Science Foundation	32/00-1
National Science Foundation	CCR-9987845

Cite this

Parnas, M., Ron, D., & Samorodnitsky, A. (2015). Proclaiming dictators and juntas or testing boolean formulae. In L. Trevisan, K. Jansen, M. Goemans, & J. D. P. Rolim (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.

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 / Luca Trevisan ; Klaus Jansen ; Michel Goemans ; Jose D. P. Rolim. Springer Verlag, 2015. pp. 273-285 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)).

@inproceedings{cfff595518504023b336db1e921035df,

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.",

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 = "2015",

language = "אנגלית",

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

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

address = "גרמניה",

}

Parnas, M, Ron, D & Samorodnitsky, A 2015, Proclaiming dictators and juntas or testing boolean formulae. in L Trevisan, K Jansen, M Goemans & JDP Rolim (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, 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.

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. / Luca Trevisan; Klaus Jansen; Michel Goemans; Jose D. P. Rolim. Springer Verlag, 2015. 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 - 2015

Y1 - 2015

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.

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

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

AN - SCOPUS:84923114993

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 - Trevisan, Luca

A2 - Jansen, Klaus

A2 - Goemans, Michel

A2 - Rolim, Jose D. P.

PB - Springer Verlag

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 Trevisan L, Jansen K, Goemans M, Rolim JDP, 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. Springer Verlag. 2015. p. 273-285. (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)).

Proclaiming dictators and juntas or testing boolean formulae

Abstract

Publication series

Conference

Bibliographical note

Funding

Other files and links

Fingerprint

Cite this