20 (2000), pp. 451–476] showed that every property that is characterized by a finite collection of forbidden induced subgraphs is -testable. However, the complexity of the test is double-tower with respect to 1/, as the only tool known to construct such tests uses a variant of Szemerédi’s regularity lemma. Here we show that any property of bipartite graphs that is characterized by a finite collection of forbidden induced subgraphs is -testable, with a number of queries that is polynomial in 1/. Our main tool is a new “conditional ” version of the regularity lemma for binary matrices, which may be interesting on its own
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