Abstract 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 ( cbfg s). 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 cbfg s should exist. This paper answers their conjecture in a positive way.