TY - JOUR

T1 - Testing monotonicity

AU - Goldreich, Oded

AU - Goldwasser, Shafi

AU - Lehman, Eric

AU - Ron, Dana

AU - Samorodnitsky, Alex

N1 - 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.

PY - 2000

Y1 - 2000

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=0038957516&partnerID=8YFLogxK

U2 - 10.1007/s004930070011

DO - 10.1007/s004930070011

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AN - SCOPUS:0038957516

SN - 0209-9683

VL - 20

SP - 301

EP - 337

JO - Combinatorica

JF - Combinatorica

IS - 3

ER -