General context-free recognition in less than cubic time
TLDR
An algorithm for general context-free recognition is given that requires less than n3 time asymptotically for input strings of length n.About:
This article is published in Journal of Computer and System Sciences.The article was published on 1975-04-01 and is currently open access. It has received 349 citations till now. The article focuses on the topics: Formal language & Computational linguistics.read more
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The Design and Analysis of Computer Algorithms
Alfred V. Aho,John E. Hopcroft +1 more
TL;DR: This text introduces the basic data structures and programming techniques often used in efficient algorithms, and covers use of lists, push-down stacks, queues, trees, and graphs.
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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.
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Models of Computation: Exploring the Power of Computing
TL;DR: In Models of Computation, John Savage re-examines theoretical computer science, offering a fresh approach that gives priority to resource tradeoffs and complexity classifications over the structure of machines and their relationships to languages.
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Program analysis via graph reachability
TL;DR: In this paper, a number of program-analysis problems can be solved by transforming them to graph reachability problems, such as program slicing, dataflow analysis, and the problem of approximating the possible shapes that heap-allocated structures in a program can take on.
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).
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An efficient context-free parsing algorithm
TL;DR: In this article, a parsing algorithm which seems to be the most efficient general context-free algorithm known is described, which is similar to both Knuth's LR(k) algorithm and the familiar top-down algorithm.
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On certain formal properties of grammars
Noam Chomsky,Noam Chomsky +1 more
TL;DR: A sequence of restrictions that limit grammars first to Turing machines, then to two types of system from which a phrase structure description of the generated language can be drawn, and finally to finite state Markov sources are shown to be increasingly heavy.
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Recognition and parsing of context-free languages in time n3*
TL;DR: A recognition algorithm is exhibited whereby an arbitrary string over a given vocabulary can be tested for containment in a given context-free language and it is shown that it is completed in a number of steps proportional to the “cube” of the number of symbols in the tested string.
An Efficient Recognition and Syntax-Analysis Algorithm for Context-Free Languages
TL;DR: It is shown in this paper that a context-free language is n cubed-recognizable in the sense of Hartmanis and Stearns and it is n to the 4th power- Recognizable by a single-head single-tape Turing machine.