Testing basic boolean formulae

Michal Parnas*, Dana Ron, Alex Samorodnitsky

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

76 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 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.

Original languageAmerican English
Pages (from-to)20-46
Number of pages27
JournalSIAM Journal on Discrete Mathematics
Volume16
Issue number1
DOIs
StatePublished - Jan 2003

Keywords

  • Approximation algorithms
  • Boolean functions
  • Property testing
  • Randomized algorithms

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