Learning conjunctive grammars and contextual binary feature grammars

Abstract

Approaches based on the idea generically called distributional learning have been making great success in the algorithmic learning of context-free languages and their extensions. We in this paper show that conjunctive grammars are also learnable by a distributional learning technique. Conjunctive grammars are context-free grammars enhanced with conjunctive rules to extract the intersection of two languages. We also compare our result with the closely related work by Clark et al. (JMLR 2010) on contextual binary feature grammars (CBFGs). Our learner is stronger than theirs. In particular our learner learns every exact CBFG, while theirs does not. Clark et al. emphasized the importance of exact CBFGs but they only conjectured there should be a learning algorithm for exact CBFGs. This paper shows that their conjecture is true.