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.