Combinatorica

, Volume 20, Issue 3, pp 301–337 | Cite as

Testing Monotonicity

  • Oded Goldreich
  • Shafi Goldwasser
  • Eric Lehman
  • Dana Ron
  • Alex Samorodnitsky
Original Paper

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.

AMS Subject Classification (1991) Classes:  68Q25, 68R05, 68Q05 

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Copyright information

© János Bolyai Mathematical Society, 2000

Authors and Affiliations

  • Oded Goldreich
    • 1
  • Shafi Goldwasser
    • 2
  • Eric Lehman
    • 3
  • Dana Ron
    • 4
  • Alex Samorodnitsky
    • 5
  1. 1.Department of Computer Science and Applied Mathematics, Weizmann Institute of Science; Rehovot, Israel; E-mail: oded@wisdom.weizmann.ac.ilIL
  2. 2.Laboratory for Computer Science, MIT; 545 Technology Sq., Cambridge, MA 02139, USA; E-mail: shafi@theory.lcs.mit.eduUS
  3. 3.Laboratory for Computer Science, MIT; 545 Technology Sq., Cambridge, MA 02139, USA; E-mail: e_lehman@theory.lcs.mit.eduUS
  4. 4.Department of EE – Systems, Tel Aviv University; Ramat Aviv, Israel; E-mail: danar@eng.tau.ac.ilIL
  5. 5.School of Mathematics, Institute for Advanced Study; Olden Lane, Princeton, NJ 08540, USA; E-mail: asamor@ias.eduUS

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