Reversible Automata and Induction of the English Auxiliary System

In this paper we apply some recent work of Angluin (1982) to the induction of the English auxiliary verb system. In general, the induction of finite automata is computationally intractable. However, Angluin shows that restricted finite automata, the kreversible automata, can he learned by efficient (polynomial time) algorithms. We present an explicit computer model demonstrating that the English auxiliary verb system can in fact be learned as a 1-reversible automaton, and hence in a computationally feasible amount of time. The entire system can be acquired by looking at only half the possible auxiliary verb sequences, and the pattern of generalization seems compatible with what is known about human acquisition of"auxiliaries. We conclude that certain linguistic subsystems may well be learnable by inductive inference methods of this kind, and suggest an extension to context-free languages.