Simple DFA are Polynomially Probably Exactly Learnable from Simple Examples

E cient learning of DFA is a challenging research problem in grammatical inference. Both exact and approximate (in the PAC sense) identi ability of DFA from examples is known to be hard. Pitt, in his seminal paper posed the following open research problem: \Are DFA PAC-identi able if examples are drawn from the uniform distribution, or some other known simple distribution?" (Pitt, 1989). We demonstrate that the class of simple DFA (i.e., DFA whose canonical representations have logarithmic Kolmogorov complexity) is e ciently probably exactly learnable under the Solomono Levin universal distribution m(wherein an instance x with Kolmogorov complexity K(x) is sampled with probability that is proportional to 2;K(x) ). The simple distribution independent learning theorem states that a concept class is learnable under the universal distribution m i it is learnable under the entire class of simple distributions provided the examples are drawn accordingto the universaldistribution (Li &a...

• Type: Conference
• Year: 1999
• Where: ICML
• Authors: Rajesh Parekh, Vasant Honavar
• Keywords: ICML 1999, Logarithmic Kolmogorov Complexity, Machine Learning, Simple Dfa, Simple Distributions