Testing monotonicity

Oded Goldreich, Shafi Goldwasser, Eric Lehman, Dana Ron, Alex Samorodnitsky

Research output: Contribution to journalArticlepeer-review

171 Scopus citations

Abstract

We present a (randomized) test for monotonicity of Boolean functions. Namely, given the ability to query an unknown function f : (0,1)n → (0,1) at arguments of its choice, the test always accepts a monotone f, and rejects f with high probability if it is ∈-far from being monotone (i.e., every monotone function differs from f on more than an ∈ fraction of the domain). The complexity of the test is O(n/∈). The analysis of our algorithm relates two natural combinatorial quantities that can be measured with respect to a Boolean function; one being global to the function and the other being local to it. A key ingredient is the use of a switching (or sorting) operator on functions.

Original languageEnglish
Pages (from-to)301-337
Number of pages37
JournalCombinatorica
Volume20
Issue number3
DOIs
StatePublished - 2000
Externally publishedYes

Bibliographical note

Funding Information:
* A preliminary (and weaker) version of th is work appeared in [25] † Work done wh ile visiting LCS, MIT. ‡Supported in part by DARPA grant DABT63-96-C-0018 an in part by a Guastella fellowsh ip. § Th is work was done wh ile visiting LCS, MIT, and was supported by an ONR Science Sch olar Fellowsh ip at th e Bunting Institute.

Funding

* A preliminary (and weaker) version of th is work appeared in [25] † Work done wh ile visiting LCS, MIT. ‡Supported in part by DARPA grant DABT63-96-C-0018 an in part by a Guastella fellowsh ip. § Th is work was done wh ile visiting LCS, MIT, and was supported by an ONR Science Sch olar Fellowsh ip at th e Bunting Institute.

FundersFunder number
Office of Naval Research
Defense Advanced Research Projects AgencyDABT63-96-C-0018

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