On parsing coupled-context-free languages
Theoretical Computer Science
Independent parallelism in finite copying parallel rewriting systems
Theoretical Computer Science
Data compression via textual substitution
Journal of the ACM (JACM)
An Improved Context-Free Recognizer
ACM Transactions on Programming Languages and Systems (TOPLAS)
An efficient context-free parsing algorithm
Communications of the ACM
Context-Free Grammars: Covers, Normal Forms, and Parsing
Context-Free Grammars: Covers, Normal Forms, and Parsing
Journal of Automata, Languages and Combinatorics - Special issue: selected papers of the second internaional workshop on Descriptional Complexity of Automata, Grammars and Related Structures (London, Ontario, Canada, July 27-29, 2000)
Introduction To Automata Theory, Languages, And Computation
Introduction To Automata Theory, Languages, And Computation
Application of Lempel--Ziv factorization to the approximation of grammar-based compression
Theoretical Computer Science
An efficient implementation of the head-corner parser
Computational Linguistics
ACL '89 Proceedings of the 27th annual meeting on Association for Computational Linguistics
Compilers: Principles, Techniques, and Tools (2nd Edition)
Compilers: Principles, Techniques, and Tools (2nd Edition)
Efficient parsing of highly ambiguous context-free grammars with bit vectors
COLING '04 Proceedings of the 20th international conference on Computational Linguistics
Deterministic left corner parsing
SWAT '70 Proceedings of the 11th Annual Symposium on Switching and Automata Theory (swat 1970)
Better binarization for the CKY parsing
EMNLP '08 Proceedings of the Conference on Empirical Methods in Natural Language Processing
Efficient parsing for transducer grammars
NAACL '09 Proceedings of Human Language Technologies: The 2009 Annual Conference of the North American Chapter of the Association for Computational Linguistics
Optimal reduction of rule length in linear context-free rewriting systems
NAACL '09 Proceedings of Human Language Technologies: The 2009 Annual Conference of the North American Chapter of the Association for Computational Linguistics
Binarization of synchronous context-free grammars
Computational Linguistics
Efficient parsing of well-nested linear context-free rewriting systems
HLT '10 Human Language Technologies: The 2010 Annual Conference of the North American Chapter of the Association for Computational Linguistics
Grammar factorization by tree decomposition
Computational Linguistics
A generalized view on parsing and translation
IWPT '11 Proceedings of the 12th International Conference on Parsing Technologies
IEEE Transactions on Information Theory
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Grammar binarization is the process and result of transforming a grammar to an equivalent form whose rules contain at most two symbols in their right-hand side. Binarization is used, explicitly or implicity, by a wide range of parsers for context-free grammars and other grammatical formalisms. Non-trivial grammars can be binarized in multiple ways, but in order to optimize the parser's computational cost, it is convenient to choose a binarization that is as small as possible. While several authors have explored heuristics to obtain compact binarizations, none of them guarantee that the resulting grammar has minimum size. However, to our knowledge, no hardness results for this problem have been published. In this article, we address this issue and prove that the problem of finding a minimum binarization of a given context-free grammar is NP-hard, by reduction from vertex cover. We also provide a lower bound on the approximability of this problem.