A Cubic Time Extension of Context-Free Grammars

Context-free grammars and cubic parse time are so related in people's minds that they often think that parsing any extension of context-free grammars must need some extra time. Of course, this is not necessarily true and this paper presents a generalization of context-free grammars which nonetheless still has a cubic parse time complexity. This extension, which defines a subclass of context-sensitive languages, has both a theoretical and a practical interest. The class of languages defined by these grammars is closed under both intersection and complement (in fact this class contains both the intersection and the complement of context-free languages). Moreover, these languages belong to an extension of mildly context-sensitive languages in which the constant growth property is relaxed and which can thus potentially be used in natural language processing.

[1]  David J. Weir,et al.  The convergence of mildly context-sensitive grammar formalisms , 1990 .

[2]  Stuart M. Shieber,et al.  Evidence against the context-freeness of natural language , 1985 .

[3]  David J. Weir,et al.  Characterizing Structural Descriptions Produced by Various Grammatical Formalisms , 1987, ACL.

[4]  Arto Salomaa,et al.  Formal languages , 1973, Computer science classics.

[5]  Aravind K. Joshi,et al.  A study of tree adjoining grammars , 1987 .

[6]  William C. Rounds,et al.  LFP A Logic for Linguistic Descriptions and an Analysis of its Complexity , 1988, Comput. Linguistics.

[7]  David J. Weir,et al.  Characterizing mildly context-sensitive grammar formalisms , 1988 .

[8]  Gerald Gazdar,et al.  Applicability of Indexed Grammars to Natural Languages , 1988 .

[9]  Pierre Boullier,et al.  A generalization of mildly context-sensitive formalisms , 1998, TAG+.

[10]  Walter J. Savitch,et al.  A Formal Model for Context-Free Languages Augmented with Reduplication , 1989, CL.

[11]  Giorgio Satta,et al.  Tree-Adjoining Grammar Parsing and Boolean Matrix Multiplication , 1994, Comput. Linguistics.

[12]  Mark Steedman,et al.  Combinatory grammars and parasitic gaps , 1987 .

[13]  Pierre Boullier,et al.  On TAG and Multicomponent TAG Parsing , 1998 .

[14]  Lothar Schmitz,et al.  An Efficient Recognizer for the Boolean Closure of Context-Free Languages , 1991, Theor. Comput. Sci..

[15]  Pierre Boullier,et al.  Range Concatenation Grammars , 2000, IWPT.

[16]  Carl Jesse Pollard,et al.  Generalized phrase structure grammars, head grammars, and natural language , 1984 .

[17]  Pierre Boullier,et al.  Chinese Numbers, MIX, Scrambling, and Range Concatenation Grammars , 1999, EACL.

[18]  David J. Weir,et al.  D-Tree Grammars , 1995, ACL.

[19]  Jay Earley,et al.  An efficient context-free parsing algorithm , 1970, Commun. ACM.

[20]  Pierre Boullier.  A Proposal for a Natural Lan-guage Processing Syntactic Backbone , 1997 .

[21]  Pierre Boullier.  On TAG parsing , 2000 .

[22]  Jeffrey D. Ullman,et al.  Introduction to Automata Theory, Languages and Computation , 1979 .