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 language | English |
|---|---|
| Pages (from-to) | 301-337 |
| Number of pages | 37 |
| Journal | Combinatorica |
| Volume | 20 |
| Issue number | 3 |
| DOIs | |
| State | Published - 2000 |
| Externally published | Yes |
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.