Skip to main content
Log in

Testing Monotonicity

  • Original Paper
  • Published:
Combinatorica Aims and scope Submit manuscript

at arguments of its choice, the test always accepts a monotone f, and rejects f with high probability if it is ε-far from being monotone (i.e., every monotone function differs from f on more than an ε fraction of the domain). The complexity of the test is O(n/ε).

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.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Similar content being viewed by others

Author information

Authors and Affiliations


Additional information

Received March 29, 1999

Rights and permissions

Reprints and permissions

About this article

Cite this article

Goldreich, O., Goldwasser, S., Lehman, E. et al. Testing Monotonicity. Combinatorica 20, 301–337 (2000).

Download citation

  • Issue Date:

  • DOI: