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 -