Learning DFA from Simple Examples

Abstract

We present a framework for learning DFA from simple examples. We show that efficient 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-identifiable 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 efficient 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 efficient PAC learning of DFAs. 1 Introduction The problem of learning a DFA with the smallest number of states that is consistent with a given sample (i.e., the DFA accepts each positive example an..