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Partially ordered multiset context-free grammars and free-word-order parsing

Giorgio Satta, Stuart M. Shieber

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Abstract

We present a new formalism, partially ordered multiset context-free grammars (poms-CFG), along with an Earley-style parsing algorithm. The formalism, which can be thought of as a generalization of context-free grammars with partially ordered right-hand sides, is of interest in its own right, and also as infrastructure for obtaining tighter complexity bounds for more expressive context-free formalisms intended to express free or multiple word-order, such as ID/LP grammars. We reduce ID/LP grammars to poms-grammars, thereby getting finer-grained bounds on the parsing complexity of ID/LP grammars. We argue that in practice, the width of attested ID/LP grammars is small, yielding effectively polynomial time complexity for ID/LP grammar parsing.

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What this paper is about

We present a new formalism, partially ordered multiset context-free grammars (poms-CFG), along with an Earley-style parsing algorithm. The formalism, which can be thought of as a generalization of context-free grammars with partially ordered right-hand sides, is of interest in its own right, and also as infrastructure for obtaining tighter complexity bounds for more expressive context-free formalisms intended to express free or multiple word-order, such as ID/LP grammars. We reduce ID/LP grammars to poms-grammars, thereby getting finer-grained bounds on the parsing complexity of ID/LP grammars. We argue that in practice, the width of attested ID/LP grammars is small, yielding effectively polynomial time complexity for ID/LP grammar parsing.

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Available abstract

We present a new formalism, partially ordered multiset context-free grammars (poms-CFG), along with an Earley-style parsing algorithm. The formalism, which can be thought of as a generalization of context-free grammars with partially ordered right-hand sides, is of interest in its own right, and also as infrastructure for obtaining tighter complexity bounds for more expressive context-free formalisms intended to express free or multiple word-order, such as ID/LP grammars. We reduce ID/LP grammars to poms-grammars, thereby getting finer-grained bounds on the parsing complexity of ID/LP grammars. We argue that in practice, the width of attested ID/LP grammars is small, yielding effectively polynomial time complexity for ID/LP grammar parsing.

Key concepts: L-attributed grammar, Phrase structure grammar, S-attributed grammar, Multiset, Indexed grammar, Tree-adjoining grammar, Parsing expression grammar, Context-free grammar

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