Parsing by matrix multiplication generalized to Boolean grammars
TLDR
The well-known parsing algorithm for context-free grammars due to Valiant (1975) is analyzed and extended to handle the more general Boolean Grammars, which are context- free grammar augmented with conjunction and negation operators in the rules.About:
This article is published in Theoretical Computer Science.The article was published on 2014-01-01 and is currently open access. It has received 38 citations till now. The article focuses on the topics: Boolean expression & Product term.read more
Citations
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Journal ArticleDOI
An extension of context-free grammars with one-sided context specifications
Mikhail Barash,Alexander Okhotin +1 more
TL;DR: Two equivalent definitions of grammars with left contexts are given and their basic properties are established, including a transformation to a normal form and a cubic-time parsing algorithm, with a square-time version for unambiguous Grammars.
Proceedings ArticleDOI
Context-free path querying by matrix multiplication
Rustam Azimov,Semyon Grigorev +1 more
TL;DR: This work proposes the first generalization of matrix-based Valiant'scontext-free language recognition algorithm for context-free path querying, and shows that the evaluation on a set of conventional benchmarks shows, that the algorithm outperforms the existing ones.
Journal ArticleDOI
Certified Context-Free Parsing: A formalisation of Valiant's Algorithm in Agda
TL;DR: This paper presents an algebraic specification, implementation, and proof of correctness of a generalisation of Valiant's algorithm that can be used for recognition, parsing or generic calculation of the transitive closure of upper triangular matrices.
Journal ArticleDOI
Generalized LR Parsing Algorithm for Grammars with One-Sided Contexts
TL;DR: The Generalized LR parsing algorithm is extended to the case of “grammars with left contexts” and has the same worst-case cubic-time performance as in the cases of context-free grammars.
Journal ArticleDOI
Input-driven languages are linear conjunctive
TL;DR: This paper demonstrates the containment of the languages accepted by input-driven pushdown automata in the family of linear conjunctive languages, which is established by a direct simulation of an input- driven automaton by a one-way real-time cellular automaton.
References
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Journal ArticleDOI
Gaussian elimination is not optimal
TL;DR: In this paper, Cook et al. gave an algorithm which computes the coefficients of the product of two square matrices A and B of order n with less than 4. 7 n l°g 7 arithmetical operations (all logarithms in this paper are for base 2).
Journal ArticleDOI
Matrix multiplication via arithmetic progressions
Don Coppersmith,Shmuel Winograd +1 more
TL;DR: In this article, a new method for accelerating matrix multiplication asymptotically is presented, based on the ideas of Volker Strassen, by using a basic trilinear form which is not a matrix product.
Book
Introduction to formal language theory
TL;DR: This volume intended to serve as a text for upper undergraduate and graduate level students and special emphasis is given to the role of algebraic techniques in formal language theory through a chapter devoted to the fixed point approach to the analysis of context-free languages.
Proceedings ArticleDOI
Multiplying matrices faster than coppersmith-winograd
TL;DR: An automated approach for designing matrix multiplication algorithms based on constructions similar to the Coppersmith-Winograd construction is developed and a new improved bound on the matrix multiplication exponent ω<2.3727 is obtained.
Gaussian Elimination is not Optimal
TL;DR: In this paper, Cook et al. gave an algorithm which computes the coefficients of the product of two square matrices A and B of order n with less than 4. 7 n l°g 7 arithmetical operations (all logarithms in this paper are for base 2).