  A computational system implemented exclusively through the spiking of neurons
was recently shown capable of syntax, that is, of carrying out the dependency
parsing of simple English sentences. We address two of the most important
questions left open by that work: constituency (the identification of key parts
of the sentence such as the verb phrase) and the processing of dependent
sentences, especially center-embedded ones. We show that these two aspects of
language can also be implemented by neurons and synapses in a way that is
compatible with what is known, or widely believed, about the structure and
function of the language organ. Surprisingly, the way we implement center
embedding points to a new characterization of context-free languages.
