Intersection Optimization is NP Complete

We propose a method for lexical disambiguation based on polarities found in several grammatical formalisms which require multi- ples intersection of finite state automata. We then prove that there is no efficient technique to minimize the state complexity of these intersec- tions.

[1]  Michael Moortgat,et al.  Categorial Type Logics , 1997, Handbook of Logic and Language.

[2]  Yves Schabes,et al.  Applying a Finite-State Intersection Grammar , 1997 .

[3]  Sheng Yu,et al.  The State Complexities of Some Basic Operations on Regular Languages , 1994, Theor. Comput. Sci..

[4]  Bruno Guillaume,et al.  Polarization and abstraction of grammatical formalisms as methods for lexical disambiguation , 2004, COLING.

[5]  Sylvain Kahane.  Polarized Unification Grammars , 2006, ACL.

[6]  Richard J. Lipton,et al.  On the complexity of intersecting finite state automata , 2000, Proceedings 15th Annual IEEE Conference on Computational Complexity.

[7]  Pasi Tapanainen.  Applying a finite-state intersection grammar , 1997 .

[8]  Julian M. Kupiec,et al.  Robust part-of-speech tagging using a hidden Markov model , 1992 .

[9]  Bernard Mérialdo,et al.  Tagging English Text with a Probabilistic Model , 1994, CL.

[10]  Anssi Yli-Jyrä,et al.  Simplification of Intermediate Results during Intersection of Multiple Weighted Automata , 2005 .

[11]  Johan van Benthem,et al.  Handbook of Logic and Language , 1996 .

[12]  Arto Salomaa,et al.  State complexity of combined operations , 2007, Theor. Comput. Sci..

[13]  Richard M. Schwartz,et al.  Coping with Ambiguity and Unknown Words through Probabilistic Models , 1993, CL.

[14]  G. Perrier,et al.  La sémantique dans les grammaires d’interaction , 2004, JEPTALNRECITAL.

[15]  Christel Baier,et al.  Weighted Automata - Theory and Applications , 2006 .

[16]  Emmanuel Roche,et al.  Finite-State Language Processing , 1997 .