  The RPNI algorithm (Oncina, Garcia 1992) constructs deterministic finite
automata from finite sets of negative and positive example words. We propose
and analyze an extension of this algorithm to deterministic $\omega$-automata
with different types of acceptance conditions. In order to obtain this
generalization of RPNI, we develop algorithms for the standard acceptance
conditions of $\omega$-automata that check for a given set of example words and
a deterministic transition system, whether these example words can be accepted
in the transition system with a corresponding acceptance condition. Based on
these algorithms, we can define the extension of RPNI to infinite words. We
prove that it can learn all deterministic $\omega$-automata with an informative
right congruence in the limit with polynomial time and data. We also show that
the algorithm, while it can learn some automata that do not have an informative
right congruence, cannot learn deterministic $\omega$-automata for all regular
$\omega$-languages in the limit. Finally, we also prove that active learning
with membership and equivalence queries is not easier for automata with an
informative right congruence than for general deterministic $\omega$-automata.
