Context-Sensitive Node Admissibility

Abstract

McCawley introduced the notion of `node admissibility conditions' as a way of studying the duality between generation and analysis, especially for context-free grammars. Subsequently, Peters and Ritchie formalized a `reasonable' generalization of context-free node admissibility for context-sensitive analysis and then proved that any language analyzable by a set of such context-sensitive node admissibility conditions is a context-free language. In this paper, I propose a stronger notion of context-sensitive node admissibility, in which local contextual dependencies are overtly represented and subject to a global consistency condition – a condition motivated by the relations among the elements in the frontier of a tree rewriting system for context-sensitive grammars. I show that this notion is adequate for context-sensitive grammars in the sense that a language is analyzable relative to this stronger notion if and only if it is generated by a context-sensitive grammar.