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

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.
