Abstract
In general property testing, we are given oracle access to a function f, and we wish to randomly 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 distance function. 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 property tester query complexity and we finetune the exponential dependence on the dimension d.
This work was supported in part by NSF grant CCR-0306283 and ARO Grant DAAH04-96-1-0181.
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Ailon, N., Chazelle, B. (2005). Information Theory in Property Testing and Monotonicity Testing in Higher Dimension. In: Diekert, V., Durand, B. (eds) STACS 2005. STACS 2005. Lecture Notes in Computer Science, vol 3404. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-31856-9_36
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DOI: https://doi.org/10.1007/978-3-540-31856-9_36
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