Polynomial Identification of $$\omega $$-Automata

Abstract

AbstractWe study identification in the limit using polynomial time and data for models of $$\omega $$-automata. On the negative side we show that non-deterministic $$\omega $$-automata (of types Büchi, coBüchi, Parity or Muller) can not be polynomially learned in the limit. On the positive side we show that the $$\omega $$-language classes $$\mathbb {IB}$$, $$\mathbb {IC}$$, $$\mathbb {IP}$$, and $$\mathbb {IM}$$ 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.