Implementation issues in the Fourier transform algorithm

The Fourier transform of Boolean functions has received considerable attention in the last few years in the computational learning theory community, and has come to play an important role in proving many important learnability results. The aim of this work is to demonstrate that the Fourier transform techniques are also a useful and practical algorithm, in addition to having many interesting theoretical properties. In fact, this work was prompted by a genuine problem that was brought to our attention; researchers at a company were trying to come by a method to reverse-engineer a state-free controller. They had the capability of querying the controller on any input, thus setting them in the membership query model, in which the Fourier transform algorithm is set. In order to keep the algorithm run-time reasonable and still produce accurate hypotheses, we had to perform many optimizations. In the paper we discuss the more prominent optimizations, ones that were crucial and without which the performance of the algorithm would severely deteriorate. One of the benefits we present is the confidence level the algorithm produces in addition to the predictions. The confidence level measures the likelihood that the prediction is correct.