EFFICIENT LEARNING OF TYPICAL FINITE AUTOMATA FROM RANDOM-WALKS

This paper describes new and efficient algorithms for learning determi nistic finite automata. Our approach is primarily distinguished by two features: (1) the adoption of an average-case setting to model the '' typical'' labeling of a finite automaton, while retaining a worst-case model for the underlying graph of the automaton, along with (2) a lea rning model in which the learner is not provided with the means to exp eriment with the machine, but rather must learn solely by observing th e automaton's output behavior on a random input sequence. The main con tribution of this paper is in presenting the first efficient algorithm s for learning nontrivial classes of automata in an entirely passive l earning model. We adopt an on-line learning model in which the learner is asked to predict the output of the next state, given the next symb ol of the random input sequence; the goal of the learner is to make as few prediction mistakes as possible. Assuming the learner has a means of resetting the target machine to a fixed start state, we first pres ent an efficient algorithm that makes an expected polynomial number of mistakes in this model. Next, we show how this first algorithm can be used as a subroutine by a second algorithm that also makes a polynomi al number of mistakes even in the absence of a reset. Along the way, w e prove a number of combinatorial results for randomly labeled automat a. We also show that the labeling of the states and the bits of the in put sequence need not be truly random, but merely semi-random. Finally , we discuss an extension of our results to a model in which automata are used to represent distributions over binary strings. (C) 1997 Acad emic Press.