Proceedings 39th Annual Symposium on Foundations of Computer Science (Cat. No.98CB36280) (1998)

Palo Alto, California

Nov. 8, 1998 to Nov. 11, 1998

ISSN: 0272-5428

ISBN: 0-8186-9172-7

pp: 426

Oded Goldreich , Weizmann Institute

Shafi Goldwasser , MIT

Eric Lehman , MIT

Dana Ron , MIT

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 epsilon-far from being monotone (i.e., every monotone function differs from f on more than an epsilon fraction of the domain). The complexity of the test is poly(n/epsilon).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.We also consider the problem of testing monotonicity based only on random examples labeled by the function. We show an Omega(\sqrt{2^n/epsilon}) lower bound on the number of required examples, and provide a matching upper bound (via an algorithm).

INDEX TERMS

Property Testing, Monotonicity, Randomized Algorithms, Approximation Algorithms.

CITATION

S. Goldwasser, E. Lehman, O. Goldreich and D. Ron, "Testing Monotonicity,"

*Proceedings 39th Annual Symposium on Foundations of Computer Science (Cat. No.98CB36280)(FOCS)*, Palo Alto, California, 1998, pp. 426.

doi:10.1109/SFCS.1998.743493

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