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 μ 2 -distinguishable Using an analog 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.