Learning DFA for Simple Examples

We present a framework for learning DFA from simple examples. We show that e cient PAC learning of DFA is possible if the class of distributions is restricted to simple distributions where a teacher might choose examples based on the knowledge of the target concept. This answers an open research question posed in Pitt's seminal paper: Are DFA's PAC-identi able if examples are drawn from the uniform distribution, or some other known simple distribution?. Our approach uses the RPNI algorithm for learning DFA from labeled examples. In particular, we describe an e cient learning algorithm for exact learning of the target DFA with high probability when a bound on the number of states (N) of the target DFA is known in advance. When N is not known, we show how this algorithm can be used for e cient PAC learning of DFAs.