Efficient learnability using the state merging algorithm is known for a subclass of probabilistic automata termed μ-distinguishable. In this paper, we prove that state merging algorithms can be extended to efficiently learn a larger class of automata. In particular, we show learnability of a subclass which we call μ_2-distinguishable. Using an ana-log of the Myhill-Nerode theorem for probabilistic automata, we analyze μ-distinguishability and generalize it to μ_p-distinguishability. By combining new results from property testing with the state merging algorithm we obtain KL-PAC learnability of the new automata class.
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