Matrix multiplication via arithmetic progressions
Journal of Symbolic Computation - Special issue on computational algebraic complexity
Two Families of Languages Related to ALGOL
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)
The Complexity of Problems Concerning Graphs with Regularities (Extended Abstract)
Proceedings of the Mathematical Foundations of Computer Science 1984
Word problems requiring exponential time(Preliminary Report)
STOC '73 Proceedings of the fifth annual ACM symposium on Theory of computing
STRING-MATCHING AND OTHER PRODUCTS
STRING-MATCHING AND OTHER PRODUCTS
Information and Computation
The Complexity of Membership Problems for Circuits Over Sets of Natural Numbers
Computational Complexity
Information and Computation
Well-founded semantics for Boolean grammars
Information and Computation
SIAM Journal on Computing
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
Equivalence Problems for Circuits over Sets of Natural Numbers
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
Fast on-line integer multiplication
Journal of Computer and System Sciences
Satisfiability of algebraic circuits over sets of natural numbers
Discrete Applied Mathematics
Fast parsing for Boolean grammars: a generalization of Valiant's algorithm
DLT'10 Proceedings of the 14th international conference on Developments in language theory
Complexity of Equations over Sets of Natural Numbers
Theory of Computing Systems
One-Nonterminal Conjunctive Grammars over a Unary Alphabet
Theory of Computing Systems
On the expressive power of univariate equations over sets of natural numbers
Information and Computation
Multiplying matrices faster than coppersmith-winograd
STOC '12 Proceedings of the forty-fourth annual ACM symposium on Theory of computing
Parsing by matrix multiplication generalized to Boolean grammars
Theoretical Computer Science
| Hi-index | 5.23 |
Consider context-free grammars generating strings over a one-letter alphabet. For the membership problem for such grammars, stated as ''Given a grammar G and a string a^n, determine whether a^n is generated by G'', only a naive O(|G|@?n^2)-time algorithm is known. This paper develops a new algorithm solving this problem, which is based upon fast multiplication of integers, works in time |G|@?nlog^3n@?2^O^(^l^o^g^^^*^n^), and is applicable to context-free grammars augmented with Boolean operations, known as Boolean grammars. For unambiguous grammars, the running time of the algorithm is reduced to |G|@?nlog^2n@?2^O^(^l^o^g^^^*^n^). The algorithm is based upon (a simplification of) the online integer multiplication algorithm by Fischer and Stockmeyer [M.J. Fischer, L.J. Stockmeyer, Fast on-line integer multiplication, Journal of Computer and System Sciences 9 (3) (1974) 317-331].