On Mildly Context-Sensitive Non-Linear Rewriting

Abstract

This paper is concerned with the relation between mild context-sensitivity and the class of languages generated by Linear Context-Free Rewriting Systems (LCFRSs). We show that there are languages that are polynomial and of constant growth but that are not LCFRLs. Starting from this observation, we define an extension of LCFRS that, roughly, allows for a limited amount of copying (or intersection, if considered in a bottom-up perspective). The proposed LCFRS extension, Literal Movement Grammars of constant non-linearity (CNL-LMG) is such that the parts that are copied into different places during a derivation cannot increase when iterating the non-linear parts of a derivation. We show that this condition guarantees that the string languages are still of constant growth. As a consequence, CNL-LMG is mildly context-sensitive while properly extending LCFRS. This result suggests that a limited and controlled amount of copying and intersection can remain tractable since it does not lead outside mild context-sensitivity. Furthermore, we show that there are natural language phenomena (in particular gapping and scrambling) where such a limited possibility of intersection gives the necessary expressive power beyond LCFRS to model these phenomena.