Efficiency of pregroups and the French noun phrase

Abstract
We study mathematical and algorithmic properties of Lambek's pregroups and illustrate them by the French noun phrase. An algorithm of complexity n3 to solve the reduction problem in an arbitrary free pregroup as well as recognition by a pregroup grammar is presented. This algorithm is then specified to run in linear time. A sufficient condition for a language fragment that makes the linear algorithm complete is given.
Keywords categorial grammars  pregroups  decision procedure  recognition algorithm  algorithmic complexity  French noun phrase
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