On the spectra of syntactic structures (Isabella Senturia, Yale University)

We explore the application of spectral graph theory to the problem of characterizing linguistically-significant classes of tree structures. We focus on various classes of syntactically-defined tree graphs, and show that the spectral properties of different matrix representations of these classes of trees provide insight into the linguistic properties that characterize these classes. More generally, our goal is to provide another route to understanding the mathematical structure of natural language, one that does not come from extensive definitions and rules defined via linguistic extrapolation, but instead is extracted directly from computation on the syntactically-defined graphical structures.