Learning one-counter languages in polynomial time

We demonstrate that the class of languages accepted by deterministic one-counter machines, or DOCAs (a natural subset of the context-free languages), is learnable in polynomial time. Our learning protocol is based upon Angluin's concept of a "minimally adequate teacher" who can answer membership queries about a concept and provide counterexamples to incorrect hypothesized concepts. We also demonstrate that the problem of testing DOCAs for equivalence may be solved in polynomial time, answering a question posed by Valiant and Paterson.