FIGURE 1. Grammatical forms.

From the following article:

Recursive syntactic pattern learning by songbirds

Timothy Q. Gentner, Kimberly M. Fenn, Daniel Margoliash and Howard C. Nusbaum

Nature 440, 1204-1207 (27 April 2006)

doi:10.1038/nature04675

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a, Finite-state form (AB)n. b, Context-free form AnBn. Both grammars describe patterned sequences of elements (lower-case letters) of the sets 'A' and 'B'. Longer strings of the form (AB)n, where n gives the number of AB iterations, are produced by appending elements to the end of an n - 1 sequence. Longer strings with the form AnBn are produced by embedding elements into the centre of an n - 1 sequence. Learning of and generalization to an AnBn pattern implies the capacity to process syntactic structures generated through recursive centre-embedding. Black arrows denote insertion points for higher-order sequences. Brightly coloured squares mark the 'AB' phrase inserted at each order. Different hues denote different elements.

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