## AbstractEfficient learnability using the state merging algorithm is known for a subclass of probabilistic automata termed $\mu$-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 $\mu_{2}$-distinguishable. Using an analog of the Myhill-Nerode theorem for probabilistic automata, we analyze $\mu$-distinguishability and generalize it to $\mu_{p}$-distinguishability. By combining new results from property testing with the state merging algorithm we obtain KL-PAC learnability of the new automata class.
[Edit] |