Polynomial Identification of [Formula: see text]-Automata

We study identification in the limit using polynomial time and data for models of [Formula: see text]-automata. On the negative side we show that non-deterministic [Formula: see text]-automata (of types Büchi, coBüchi, Parity or Muller) can not be polynomially learned in the limit. On the positive side we show that the [Formula: see text]-language classes [Formula: see text], [Formula: see text], [Formula: see text], and [Formula: see text] that are defined by deterministic Büchi, coBüchi, parity, and Muller acceptors that are isomorphic to their right-congruence automata (that is, the right congruences of languages in these classes are fully informative) are identifiable in the limit using polynomial time and data. We further show that for these classes a characteristic sample can be constructed in polynomial time.