Distributional learning of conjunctive grammars and contextual binary feature grammars

Approaches based on the idea generically called distributional learning have been making great success in the algorithmic learning of several rich subclasses of context-free languages and their extensions. Those language classes are defined by properties concerning string-context relation. In this paper, we present a distributional learning algorithm for conjunctive grammars with the k-finite context property (k-FCP) for each natural number k. We also compare our result with the closely related work by Clark et al. (JMLR 2010) [5] on learning some context-free grammars using contextual binary feature grammars (CBFGs). We prove that the context-free grammars targeted by their algorithm have the k-FCP. Moreover, we show that every exact CBFG has the k-FCP, too, while not all of them are learnable by their algorithm. Clark et al. conjectured a learning algorithm for exact CBFGs should exist. This paper answers their conjecture in a positive way.