Learning DFA from Simple Examples

Efficient learning of DFA is a challenging research problem in grammatical inference. It is known that both exact and approximate (in the PAC sense) identifiability of DFA is hard. Pitt, in his seminal paper posed the following open research problem: “Are DFA PAC-identifiable if examples are drawn from the uniform distribution, or some other known simple distribution?” [25]. We demonstrate that the class of simple DFA (i.e., DFA whose canonical representations have logarithmic Kolmogorov complexity) is efficiently PAC learnable under the Solomonoff Levin universal distribution. We prove that if the examples are sampled at random according to the universal distribution by a teacher that is knowledgeable about the target concept, the entire class of DFA is efficiently PAC learnable under the universal distribution. Thus, we show that DFA are efficiently learnable under the PACS model [6]. Further, we prove that any concept that is learnable under Gold’s model for learning fro...

• Type: Conference
• Year: 1997
• Where: ALT
• Authors: Rajesh Parekh, Vasant Honavar
• Keywords: ALT 1997, Machine Learning, PAC Learnable, Research Problem, Universal Distribution