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Programming-by-example technologies are being deployed in industrial productsfor real-time synthesis of various kinds of data transformations. Thesetechnologies rely on the user to provide few representative examples of thetransformation task. Motivated by the need to find the most pertinent questionto ask the user, in this paper, we introduce the {\em significant questionsproblem}, and show that it is hard in general. We then develop aninformation-theoretic greedy approach for solving the problem. We justify thegreedy algorithm using the conditional entropy result, which informally saysthat the question that achieves the maximum information gain is the one that weknow least about.  In the context of interactive program synthesis, we use the above result todevelop an {\em{active program learner}} that generates the significant inputsto pose as queries to the user in each iteration. The procedure requiresextending a {\em{passive program learner}} to a {\em{sampling program learner}}that is able to sample candidate programs from the set of all consistentprograms to enable estimation of information gain. It also uses clustering ofinputs based on features in the inputs and the corresponding outputs to samplea small set of candidate significant inputs. Our active learner is able totradeoff false negatives for false positives and converge in a small number ofiterations on a real-world dataset of %around 800 string transformation tasks.

Information-theoretic User Interaction: Significant Inputs for Program Synthesis