Membership problems for regular and context-free trace languages
Information and Computation
Matrix multiplication via arithmetic progressions
Journal of Symbolic Computation - Special issue on computational algebraic complexity
Context-free recognition via shortest paths computation: a version of Valiant's algorithm
Theoretical Computer Science
TAL recognition in O(M(n2)) time
Journal of Computer and System Sciences
Fast context-free grammar parsing requires fast boolean matrix multiplication
Journal of the ACM (JACM)
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 Formal Language Theory
Introduction to Formal Language Theory
Tree-adjoining grammar parsing and boolean matrix multiplication
Computational Linguistics
Information and Computation
Recursive descent parsing for Boolean grammars
Acta Informatica
Matrix-vector multiplication in sub-quadratic time: (some preprocessing required)
SODA '07 Proceedings of the eighteenth annual ACM-SIAM symposium on Discrete algorithms
Information and Computation
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
Well-founded semantics for Boolean grammars
Information and Computation
Conjunctive Grammars over a Unary Alphabet: Undecidability and Unbounded Growth
Theory of Computing Systems - Special Issue: Symposium on Computer Science, Guest Editors: Sergei Artemov, Volker Diekert and Dima Grigoriev
General context-free recognition in less than cubic time
Journal of Computer and System Sciences
Complexity of Equations over Sets of Natural Numbers
Theory of Computing Systems
Multiplying matrices faster than coppersmith-winograd
STOC '12 Proceedings of the forty-fourth annual ACM symposium on Theory of computing
Parsing Boolean grammars over a one-letter alphabet using online convolution
Theoretical Computer Science
| Hi-index | 5.23 |
The well-known parsing algorithm for context-free grammars due to Valiant (1975) [25] is analyzed and extended to handle the more general Boolean grammars, which are context-free grammars augmented with conjunction and negation operators in the rules. The algorithm reduces construction of a parsing table to computing multiple products of Boolean matrices of various sizes. Its time complexity on an input string of length n is O(BMM(n)logn), where BMM(n) is the number of operations needed to multiply two Boolean matrices of size nxn, which is O(n^@w) with @w