Learnability of Probabilistic Automata via Oracles

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 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.