Using restriction to extend parsing algorithms for complex-feature-based formalisms

Grammar formalisms based on the encoding of grammatical information in complex-valued feature systems enjoy some currency both in linguistics and natural-language-processing research. Such formalisms can be thought of by analogy to context-free grammars as generalizing the notion of nonterminal symbol from a finite domain of atomic elements to a possibly infinite domain of directed graph structures of a certain sort. Unfortunately, in moving to an infinite nonterminal domain, standard methods of parsing may no longer be applicable to the formalism. Typically, the problem manifests itself as gross inefficiency or even nontermination of the algorithms. In this paper, we discuss a solution to the problem of extending parsing algorithms to formalisms with possibly infinite nonterminal domains, a solution based on a general technique we call restriction. As a particular example of such an extension, we present a complete, correct, terminating extension of Earley's algorithm that uses restriction to perform top-down filtering. Our implementation of this algorithm demonstrates the drastic elimination of chart edges that can be achieved by this technique. Finally, we describe further uses for the technique---including parsing other grammar formalisms, including definite-clause grammars; extending other parsing algorithms, including LR methods and syntactic preference modeling algorithms; and efficient indexing.