Abstract
Pregroup grammars are context-free lexicalized grammars based upon free pregroups which can describe parts of the syntax of natural languages. Some extensions are useful to model special constructions like agreements with complex features or non-projective relations or dependencies. A simple solution for these problems is given by lexicalized grammars based upon the product of free pregroups rather than on a single free pregroup. Such grammars are not necessarily context-free. However, the membership problem is NP-complete. To prove this theorem, the article defines a particular grammar built on the product of three free pregroups. This grammar is used to encode any SAT problem as a membership problem in the language corresponding to the grammar.
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Béchet, D. (2014). NP-Completeness of Grammars Based Upon Products of Free Pregroups. In: Casadio, C., Coecke, B., Moortgat, M., Scott, P. (eds) Categories and Types in Logic, Language, and Physics. Lecture Notes in Computer Science, vol 8222. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-54789-8_4
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