Learning Linearly Separable Languages

For a finite alphabet A, we define a class of embeddings of A∗ into an infinite-dimensional feature space X and show that its finitely supported hyperplanes define regular languages. This suggests a general strategy for learning regular languages from positive and negative examples. We apply this strategy to the piecewise testable languages, presenting an embedding under which these are precisely the linearly separable ones, and thus are efficiently learnable. Most of this work was done while the author was visiting the Hebrew University, Jerusalem, Israel. This work was supported in part by the IST Programme of the European Community, under the PASCAL Network of Excellence, IST-2002-506778. The research at CMU was supported in part by NSF ITR grant IIS-0205456. This publication only reflects the author’s views.