Information theory in property testing and monotonicity testing in higher dimension

Nir Ailon, Bernard Chazelle

Research output: Contribution to journalArticlepeer-review

53 Scopus citations


In property testing, we are given oracle access to a function f, and we wish to test if the function satisfies a given property P, or it is ε-far from having that property. In a more general setting, the domain on which the function is defined is equipped with a probability distribution, which assigns different weight to different elements in the domain. This paper relates the complexity of testing the monotonicity of a function over the d-dimensional cube to the Shannon entropy of the underlying distribution. We provide an improved upper bound on the query complexity of the property tester.

Original languageEnglish (US)
Pages (from-to)1704-1717
Number of pages14
JournalInformation and Computation
Issue number11
StatePublished - Nov 2006
Externally publishedYes

All Science Journal Classification (ASJC) codes

  • Theoretical Computer Science
  • Information Systems
  • Computer Science Applications
  • Computational Theory and Mathematics


  • Information theory
  • Property testing


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