Polynomial Identification of omega-Automata

Dana Angluin, Dana Fisman, Yaara Shoval

We 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 Buchi, coBuchi, Parity, Rabin, Street, or Muller) cannot be polynomially learned in the limit. On the positive side we show that the omega-language classes IB, IC, IP, IR, IS, and IM, which are defined by deterministic Buchi, coBuchi, Parity, Rabin, Streett, and Muller acceptors that are isomorphic to their right-congruence automata, are identifiable in the limit using polynomial time and data. We give polynomial time inclusion and equivalence algorithms for deterministic Buchi, coBuchi, Parity, Rabin, Streett, and Muller acceptors, which are used to show that the characteristic samples for IB, IC, IP, IR, IS, and IM can be constructed in polynomial time. We also provide polynomial time algorithms to test whether a given deterministic automaton of type X (for X in {B, C, P, R, S, M})is in the class IX (i.e. recognizes a language that has a deterministic automaton that is isomorphic to its right congruence automaton).

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