Finding Hierarchical Structure in Binary Sequences: Evidence from Lindenmayer Grammar Learning

Abstract

In this article, we explore the extraction of recursive nested structure in the processing of binary sequences. Our aim was to determine whether humans learn the higher-order regularities of a highly simplified input where only sequential-order information marks the hierarchical structure. To this end, we implemented a sequence generated by the Fibonacci grammar in a serial reaction time task. This deterministic grammar generates aperiodic but self-similar sequences. The combination of these two properties allowed us to evaluate hierarchical learning while controlling for the use of low-level strategies like detecting recurring patterns. The deterministic aspect of the grammar allowed us to predict precisely which points in the sequence should be subject to anticipation. Results showed that participants’ pattern of anticipation could not be accounted for by “flat” statistical learning processes and was consistent with them anticipating upcoming points based on hierarchical assumptions. We also found that participants were sensitive to the structure constituency, suggesting that they organized the signal into embedded constituents. We hypothesized that the participants built this structure by merging recursively deterministic transitions.