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Phrase-structure grammars are an effective representation for important syntactic and semantic aspects of natural languages, but are computationally too demanding for use as language models in real-time speech recognition. An algorithm is described that computes finite-state approximations for context-free grammars and equivalent augmented phrase-structure grammar formalisms. The approximation is exact for certain context-free grammars generating regular languages, including all left-linear and right-linear context-free grammars. The algorithm has been used to construct finite-state language models for limited-domain speech recognition tasks.