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Learnability of Probabilistic Automata via Oracles
Omri Guttman, S V N Vishwanathan and Bob Williamson
In: Algorithmic Learning Theory, 2005, 08 - 11 Oct 2005, Singapore.
Abstract Efficient 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.
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