SIGACT News complexity theory column 32

Abstract

We describe some recent or not-so-recent results in the model of learning known as exact learning from queries. Some results are chosen because they led to a result in complexity theory, and others are chosen because they seem to indicate an interesting line of research at the common ground of learning and complexity. More precisely, we survey: (1) an improvement of the Karp-Lipton collapse that stemmed from a learning algorithm for Boolean circuits, (2) recent advances in distinguishing information-theoretic from complexity-theoretic difficulty of learning, and (3) recent results on learning small-depth circuits with modular gates that call for a systematic study of the expressive power of so-called Multiplicity Automata.