Transforming Projective Bilexical Dependency Grammars into efficiently-parsable CFGs with Unfold-Fold

This paper shows how to use the UnfoldFold transformation to transform Projective Bilexical Dependency Grammars (PBDGs) into ambiguity-preserving weakly equivalent Context-Free Grammars (CFGs). These CFGs can be parsed in O(n 3 ) time using a CKY algorithm with appropriate indexing, rather than the O(n 5 ) time required by a naive encoding. Informally, using the CKY algorithm with such a CFG mimics the steps of the Eisner-Satta O(n 3 ) PBDG parsing algorithm. This transformation makes all of the techniques developed for CFGs available to PBDGs. We demonstrate this by describing a maximum posterior parse decoder for PBDGs.

[1]  Taisuke Sato,et al.  Equivalence-Preserving First-Order Unfold/Fold Transformation Systems , 1990, Theor. Comput. Sci..

[2]  Joshua Goodman,et al.  Parsing Algorithms and Metrics , 1996, ACL.

[3]  Dan Klein,et al.  Learning Accurate, Compact, and Interpretable Tree Annotation , 2006, ACL.

[4]  Jason Eisner,et al.  Bilexical Grammars and their Cubic-Time Parsing Algorithms , 2000 .

[5]  John Darlington,et al.  A Transformation System for Developing Recursive Programs , 1977, J. ACM.

[6]  Fernando Pereira,et al.  Online Learning of Approximate Dependency Parsing Algorithms , 2006, EACL.

[7]  Steve Young,et al.  Applications of stochastic context-free grammars using the Inside-Outside algorithm , 1990 .

[8]  Jiří Vyskočil,et al.  Transformation of Logic Programs , 2008 .

[9]  Alberto Pettorossi,et al.  Transformation of Logic Programs , 1994 .

[10]  Stuart M. Shieber,et al.  Prolog and Natural-Language Analysis , 1987 .

[11]  Patrick Saint-Dizier,et al.  Review of Prolog and natural-language analysis: CSLI lecture notes 10 by Fernando C. N. Pereira and Stuart M. Shieber. Center for the Study of Language and Information 1987. , 1988 .

[12]  C. Pollard,et al.  Center for the Study of Language and Information , 2022 .

[13]  Fernando Pereira,et al.  Discriminative learning and spanning tree algorithms for dependency parsing , 2006 .

[14]  Daniel H. Younger,et al.  Recognition and Parsing of Context-Free Languages in Time n^3 , 1967, Inf. Control..

[15]  Vladimir Solmon,et al.  The estimation of stochastic context-free grammars using the Inside-Outside algorithm , 2003 .

[16]  Jun'ichi Tsujii,et al.  Probabilistic CFG with Latent Annotations , 2005, ACL.

[17]  Giorgio Satta,et al.  Efficient Parsing for Bilexical Context-Free Grammars and Head Automaton Grammars , 1999, ACL.

[18]  Jason Eisner,et al.  Three New Probabilistic Models for Dependency Parsing: An Exploration , 1996, COLING.

[19]  Zhiyi Chi,et al.  Statistical Properties of Probabilistic Context-Free Grammars , 1999, CL.