Testing Monotonicity

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.

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Received March 29, 1999

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Goldreich, O., Goldwasser, S., Lehman, E. et al. Testing Monotonicity. Combinatorica 20, 301–337 (2000). https://doi.org/10.1007/s004930070011

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