Learning regular omega languages

We provide an algorithm for learning an unknown regular set of infinite words using membership and equivalence queries. Three variations of the algorithm learn three different canonical representations of regular omega languages using the notion of families of DFAs. One is of size similar to L_$, a DFA representation recently learned using L^⁎ by Farzan et al. The second is based on the syntactic FORC, introduced by Maler and Staiger. The third is introduced herein. We show that the second and third can be exponentially smaller than the first, and the third is at most as large as the second, with up to a quadratic saving with respect to the second.