Learning two-tape automata from queries and counterexamples

We investigate the learning problem of two-tape deterministic finite automata (2-tape DFAs) from queries and counterexamples. Instead of accepting a subset of Σ*, a 2-tape DFA over an alphabet Σ accepts a subset of Σ*×Σ*, and therefore, it can specify a binary relation on Σ*. In Angluin showed that the class of deterministic finite automata (DFAs) is learnable in polynomial time from membership queries and equivalence queries, namely, from minimally adequate teacher (MAT). In this article we show that the class of 2-tape DFAs is learnable in polynomial time from MAT in the following sense that there effectively exists an algorithm that, given any language L accepted by an unknown 2-tape DFA M, learns from MAT a two-tape nondeterministic finite automaton (2-tape NFA) M′ accepting L in time polynomial in n and l, where n is the size of M for L and l is the maximum length of any counterexample provided during the learning process. This gives a generalization of the corresponding Angluin's result for DFAs.