Exact Identi cation of Read - once Formulas Using Fixed Points ofAmpli cation

In this paper we describe a new technique for exactly identifying certain classes of read-once Boolean formulas. The method is based on sampling the input-output behavior of the target formula on a probability distribution that is determined by the xed point of the formula's ampliication function (deened as the probability that a 1 is output by the formula when each input bit is 1 independently with probability p). By performing various statistical tests on easily sampled variants of the xed-point distribution, we are able to eeciently infer all structural information about any logarithmic-depth formula (with high probability). We apply our results to prove the existence of short universal identiication sequences for large classes of formulas. We also describe extensions of our algorithms to handle high rates of noise, and to learn formulas of unbounded depth in Valiant's model with respect to speciic distributions.