Uncovering hierarchical structure through statistical dependency

Abstract

In this paper, we explore the extraction of recursive nested structure in the processing of self-similar binary sequences generated by two Lindenmayer grammars: the Fibonacci grammar and the Skip grammar. In each of these grammars only sequential order information marks the hierarchical structure. Although closely related, these grammars differ from a formal point of view: the Fibonacci grammar is perfectly scale-free and presents an isomorphism between its surface and derivational properties while the Skip grammar, although also self-similar, does not present this isomorphism. Our goal was to explore the influence of these formal differences on the extraction of hierarchical structure by the participants. To this end, we implemented these grammars in a serial reaction time task. The results show that in both the Fibonacci grammar and the Skip grammar, participants elaborated a hierarchical structure from the signal. This suggests the involvement of at least partially similar mechanisms during processing. However, some processing differences remained that cannot be explained by the hypotheses proposed so far regarding the processing of strings generated by L-systems. We hypothesize that these effects would be due to the self-similarity of the signal which would act as a reinforcement of the structure elaborated by the participants.