TY - JOUR

T1 - Testing basic boolean formulae

AU - Parnas, Michal

AU - Ron, Dana

AU - Samorodnitsky, Alex

PY - 2003/1

Y1 - 2003/1

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 would like to decide whether f ε ℱ or whether it differs from every g ε ℱ on more than an ε-fraction of the domain elements. The classes of functions we consider are singleton ("dictatorship") functions, monomials, and monotone disjunctive normal form 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 linear in 1/ε.

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 would like to decide whether f ε ℱ or whether it differs from every g ε ℱ on more than an ε-fraction of the domain elements. The classes of functions we consider are singleton ("dictatorship") functions, monomials, and monotone disjunctive normal form 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 linear in 1/ε.

KW - Approximation algorithms

KW - Boolean functions

KW - Property testing

KW - Randomized algorithms

UR - http://www.scopus.com/inward/record.url?scp=0037285627&partnerID=8YFLogxK

U2 - 10.1137/S0895480101407444

DO - 10.1137/S0895480101407444

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AN - SCOPUS:0037285627

SN - 0895-4801

VL - 16

SP - 20

EP - 46

JO - SIAM Journal on Discrete Mathematics

JF - SIAM Journal on Discrete Mathematics

IS - 1

ER -