EXACT IDENTIFICATION OF READ-ONCE FORMULAS USING FIXED-POINTS OF AMPLIFICATION FUNCTIONS

In this paper a new technique is described for exactly identifying cer tain classes of read-once Boolean formulas. The method is based on sam pling the input-output behavior of the target formula on a probability distribution that is determined by the fixed point of the formula's a mplification function (defined as the probability that a one is output by the formula when each input bit is one independently with probabil ity p). By performing various statistical tests on easily sampled vari ants of the fixed-point distribution, it is possible to efficiently in fer all structural information about any logarithmic-depth formula (wi th high probability). Results are applied to prove the existence of sh ort universal identification sequences for large classes of formulas. Also described are extensions of these algorithms to handle high rates of noise, and to learn formulas of unbounded depth in Valiant's model with respect to specific distributions.