Learnability of probabilistic automata via oracles

Authors:
Omri Guttman;S. V. N. Vishwanathan;Robert C. Williamson
Affiliations:
Statistical Machine Learning Program, National ICT Australia, RSISE, Australian National University, Canberra, ACT, Australia;Statistical Machine Learning Program, National ICT Australia, RSISE, Australian National University, Canberra, ACT, Australia;Statistical Machine Learning Program, National ICT Australia, RSISE, Australian National University, Canberra, ACT, Australia
Venue:
ALT'05 Proceedings of the 16th international conference on Algorithmic Learning Theory
Year:
2005

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Learning probabilistic automata: A study in state distinguishability

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Abstract

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.