Compilers: principles, techniques, and tools
Compilers: principles, techniques, and tools
Fast recognition of pushdown automaton and context-free languages
Information and Control
A simplified lower bound for context-free-language recognition
Information and Control
Matrix multiplication via arithmetic progressions
STOC '87 Proceedings of the nineteenth annual ACM symposium on Theory of computing
Extra high speed matrix multiplication on the Cray-2
SIAM Journal on Scientific and Statistical Computing
Matrix multiplication via arithmetic progressions
Journal of Symbolic Computation - Special issue on computational algebraic complexity
Handbook of theoretical computer science (vol. A)
Context-free recognition via shortest paths computation: a version of Valiant's algorithm
Theoretical Computer Science
Survey of the state of the art in human language technology
TAL recognition in O(M(n2)) time
Journal of Computer and System Sciences
On the Parsing of Deterministic Languages
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
Tuning Strassen's matrix multiplication for memory efficiency
SC '98 Proceedings of the 1998 ACM/IEEE conference on Supercomputing
Speech and Language Processing: An Introduction to Natural Language Processing, Computational Linguistics, and Speech Recognition
Introduction To Automata Theory, Languages, And Computation
Introduction To Automata Theory, Languages, And Computation
Introduction to Formal Language Theory
Introduction to Formal Language Theory
On the Complexity of General Context-Free Language Parsing and Recognition (Extended Abstract)
Proceedings of the 6th Colloquium, on Automata, Languages and Programming
Tree-adjoining grammar parsing and boolean matrix multiplication
Computational Linguistics
PCFG models of linguistic tree representations
Computational Linguistics
ACL '96 Proceedings of the 34th annual meeting on Association for Computational Linguistics
Packrat parsing:: simple, powerful, lazy, linear time, functional pearl
Proceedings of the seventh ACM SIGPLAN international conference on Functional programming
Parsing expression grammars: a recognition-based syntactic foundation
Proceedings of the 31st ACM SIGPLAN-SIGACT symposium on Principles of programming languages
Colored intersection searching via sparse rectangular matrix multiplication
Proceedings of the twenty-second annual symposium on Computational geometry
Efficient transitive closure of sparse matrices over closed semirings
Theoretical Computer Science - Algebraic methods in language processing
Proofs and pedagogy; science and systems: The grammar tool box
Science of Computer Programming
Fast multiplication of matrices over a finitely generated semiring
Information Processing Letters
Fast Stochastic Context-Free Parsing: A Stochastic Version of the Valiant Algorithm
IbPRIA '07 Proceedings of the 3rd Iberian conference on Pattern Recognition and Image Analysis, Part I
Restricted global grammar constraints
CP'09 Proceedings of the 15th international conference on Principles and practice of constraint programming
Typed and unambiguous pattern matching on strings using regular expressions
Proceedings of the 12th international ACM SIGPLAN symposium on Principles and practice of declarative programming
Dynamic programming for linear-time incremental parsing
ACL '10 Proceedings of the 48th Annual Meeting of the Association for Computational Linguistics
Modularization of regular growth automata
FSMNLP '11 Proceedings of the 9th International Workshop on Finite State Methods and Natural Language Processing
Vine pruning for efficient multi-pass dependency parsing
NAACL HLT '12 Proceedings of the 2012 Conference of the North American Chapter of the Association for Computational Linguistics: Human Language Technologies
A bayesian model for learning SCFGs with discontiguous rules
EMNLP-CoNLL '12 Proceedings of the 2012 Joint Conference on Empirical Methods in Natural Language Processing and Computational Natural Language Learning
On repairing structural problems in semi-structured data
Proceedings of the VLDB Endowment
Parsing by matrix multiplication generalized to Boolean grammars
Theoretical Computer Science
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In 1975, Valiant showed that Boolean matrix multiplication can be used for parsing context-free grammars (CFGs), yielding the asympotically fastest (although not practical) CFG parsing algorithm known. We prove a dual result: any CFG parser with time complexity O(gn3-∈), where g is the size of the grammar and n is the length of the input string, can be efficiently converted into an algorithm to multiply m × m Boolean matrices in time O(m3-∈/3). Given that practical, substantially subcubic Boolean matrix multiplication algorithms have been quite difficult to find, we thus explain why there has been little progress in developing practical, substantially subcubic general CFG parsers. In proving this result, we also develop a formalization of the notion of parsing.