Complexity of Grammar Induction for Quantum Types

Antonin Delpeuch
(École Normale Supérieure, Paris)

Most categorical models of meaning use a functor from the syntactic category to the semantic category. When semantic information is available, the problem of grammar induction can therefore be defined as finding preimages of the semantic types under this forgetful functor, lifting the information flow from the semantic level to a valid reduction at the syntactic level. We study the complexity of grammar induction, and show that for a variety of type systems, including pivotal and compact closed categories, the grammar induction problem is NP-complete. Our approach could be extended to linguistic type systems such as autonomous or bi-closed categories.

In Bob Coecke, Ichiro Hasuo and Prakash Panangaden: Proceedings of the 11th workshop on Quantum Physics and Logic (QPL 2014), Kyoto, Japan, 4-6th June 2014, Electronic Proceedings in Theoretical Computer Science 172, pp. 236–248.
Published: 28th December 2014.

ArXived at: http://dx.doi.org/10.4204/EPTCS.172.16 bibtex PDF
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