Generative capacity of standard grammatical formalisms for anti-context-free languages

Ascertain whether any of the established mildly context-sensitive grammar formalisms—specifically Tree Adjoining Grammars (TAG), Linear Indexed Grammars (LIG), Linear Context-Free Rewriting Systems (LCFRS), or Multiple Context-Free Grammars (MCFG)—can generate all languages in the class of anti-context-free languages (-CF), where -CF is defined as (-LC)/PR = (LC)/(-PR) via anti-local tree languages and (anti-)projective linearisations.

Background

The paper introduces a dual class to context-free languages, termed anti-context-free languages (-CF), defined via dual notions of locality and projectivity on simple dependency trees: -CF = (-LC)/PR = (LC)/(-PR). The class includes linguistically motivated non-context-free languages such as the copy language and the respectively language, and is shown to be semilinear.

In formal language theory, several well-known grammar formalisms (e.g., TAG, LIG, LCFRS, MCFG) have been proposed to capture mildly context-sensitive phenomena found in natural language. While the paper establishes structural and closure properties for -CF, it leaves open whether existing, widely studied grammatical formalisms can generate the entire class -CF.

The discussion notes that n-copy languages are in -CF, while TAG is known to generate only the 2-copy language, underscoring uncertainty about the reach of standard formalisms relative to the full expressiveness of -CF.