A basic lower bound for property testing

Abstract

An $\hat{I}\mu$-test for any non-trivial property (one for which there are both satisfying inputs and inputs of large distance from the property) should use a number of queries that is at least inversely proportional in $\hat{I}\mu$. However, to the best of our knowledge there is no reference proof for this intuition. Such a proof is provided here. It is written so as to not require any prior knowledge of the related literature, and in particular does not use Yao's method.

4 pages. Added a related work reference