Identification in the Limit of k, l-Substitutable Context-Free Languages

Recently Clark and Eyraud (2005, 2007) have shown that substitutable context-free languages are polynomial-time identifiable in the limit from positive data. Substitutability in context-free languages can be thought of as the analogue of reversibility in regular languages. While reversible languages admit a hierarchy, namely k-reversible regular languages for each nonnegative integer k, Clark and Eyraud targeted the subclass of context-free languages that corresponds to zero-reversible regular languages only. Following Clark and Eyraud's proposal, this paper introduces a hierarchy of substitutable context-free languages as the analogue of that of k-reversible regular languages and shows that each class in the hierarchy is also polynomial-time identifiable in the limit from positive data.

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