Formal Properties of Feature Grammars

This paper describes the formal power of feature grammars such as Generalised Phrase Structured Grammars (GPSG) 1]. It shows how such grammars relate to context-free grammar (Chomsky type 2) and which extensions cause the formalism to increase in power to context-sensitive grammar and beyond. Also, it describes how any Turing machine can be implemented as a feature grammar showing that the power of such grammars is beyond context-free. Finally some discussion is given on the relevance of the these results. The rst point to make, and probably the most important, is a distinction between grammar and formalism. This distinction is often blurred in computational linguistics. To give an example Grammar(1) is a particular context-free grammar. While the formalism for context-free grammars is described as ((8] p 80) A context-free grammar is 4-tuple (T; N; S; P). Where T is a nite set of terminal symbols; N is a nite set of non-terminal symbols; S is one non-terminal called the distinguished symbol; and P is nite set of production of the form A ! where A is a non-terminal and is a string of terminals and non-terminals of length one or more.