## AbstractEfficient 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 µ2-distinguishable. Using an analog of the Myhill-Nerode theorem for probabilistic automata, we analyze µ-distinguishability and generalize it to µp-distinguishability. By combining new results from property testing with the state merging algorithm we obtain KL-PAC learnability of the new automata class. Our research hints at closer connections between property testing and probabilistic automata learning and leads to very interesting open problems.
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