Learnability of Probabilistic Automata via Oracles
Omri Guttmann, S V N Vishwanathan and Bob Williamson
In: International Conference on Algorithmic Learning Theory, 8-11 October 2005, Singapore.
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.