Features Moving Madly: A Formal Perspective on Feature Percolation in the Minimalist Program

AbstractI show that adding a mechanism of feature percolation (via specifier head agreement) to Minimalist Grammars (MGs) [Stabler (1997) In Retore C. (ed.) Logical Aspects of Computational Linguistics, Springer Verlag (Lecture Notes in Computer Science 1328), NY, pp. 68–95] takes them out of the class of context-sensitive grammar formalisms. The main theorem of the paper is that adding a mechanism of feature percolation to MGs allows them to implement infinite abaci [Lambek (1961), Canadian Mathematical bulletin 4, pp. 259–302], which can simulate any Turing Machine computation. As a simple corollary, I show that, for any computable $$f\!:\mathbb{N} \rightarrow \mathbb{N}$$, MGs thus enhanced can generate the language $$L_{a^{f(n)}} = \{ a^{f(n)} : n \in \mathbb{N}\}$$.