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Comparative complexity of grammar forms

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Seymour Ginsburg,

Nancy LynchAuthors Info & Claims

STOC '75: Proceedings of the seventh annual ACM symposium on Theory of computing

Pages 153 - 158

https://doi.org/10.1145/800116.803764

Published: 05 May 1975 Publication History

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Abstract

The definition of “grammar form” introduced in [CG] makes it possible to state and prove results about various types of grammars in a uniform way. Among questions naturally formalizable in this framework are many about the complexity or efficiency of grammars of different kinds. Grammar forms provide a reasonable way of considering the totality of other forms we might use, and so answering the question with both upper and lower bound results.

The general question considered in this paper is the following: which grammar forms are more efficient than other grammar forms for the expression of classes of languages, and how much gain in efficiency is possible? Our results deal solely with context-free grammars, and use both derivation complexity and size of grammars as complexity measures.

References

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Book, R.V., "Time-Bounded Grammars and their Languages," JCSS, 5 (1971), pp. 397-429.

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[2]

Chomsky, N., "On Certain Formal Properties of Grammars," Inf. and Control, 2 (1959), pp. 137-167.

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[3]

Cremers, A. B and S. Ginsburg, "Context-Free Grammar Forms," to appear in JCSS.

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[4]

Ginsburg, S. and N.A. Lynch, "Derivation Complexity in Context-Free Grammar Forms," submitted for publication.

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[5]

Ginsburg, S. and N.A. Lynch, "Size Complexity in Context-Free Grammar Forms," in preparation.

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Gladkii, A., "On the Complexity of Derivations in Phrase-Structure Grammars," Algebra i Logika Sem. 3 (1964), pp. 29-44.

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Gruska, J., "On the Size of Context-Free Grammars," Kybernetica 8 (1972), pp. 213-218.

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Meyer, A.R. and M.J. Fischer, "Economy of Description by Automata, Grammars and Formal Systems," 12-th Annual Symposium on Switching and Automata Theory (1971), pp. 188-191.

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Gruska J(2005)Descriptional complexity (of languages) a short surveyMathematical Foundations of Computer Science 197610.1007/3-540-07854-1_162(65-80)Online publication date: 21-May-2005
https://doi.org/10.1007/3-540-07854-1_162
Greibach S(1981)Formal LanguagesIEEE Annals of the History of Computing10.1109/MAHC.1981.100063:1(14-41)Online publication date: 1-Jan-1981
https://dl.acm.org/doi/10.1109/MAHC.1981.10006
Peterson G(1980)Succinct representation random strings, and complexity classesProceedings of the 21st Annual Symposium on Foundations of Computer Science10.1109/SFCS.1980.42(86-95)Online publication date: 13-Oct-1980
https://dl.acm.org/doi/10.1109/SFCS.1980.42
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Index Terms

Comparative complexity of grammar forms
1. Theory of computation
  1. Computational complexity and cryptography
    1. Complexity classes
  2. Formal languages and automata theory
    1. Formalisms
      1. Rewrite systems
    2. Grammars and context-free languages

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STOC '75: Proceedings of the seventh annual ACM symposium on Theory of computing

May 1975

265 pages

ISBN:9781450374194

DOI:10.1145/800116

Permission to make digital or hard copies of all or part of this work for personal or classroom use is granted without fee provided that copies are not made or distributed for profit or commercial advantage and that copies bear this notice and the full citation on the first page. Copyrights for components of this work owned by others than ACM must be honored. Abstracting with credit is permitted. To copy otherwise, or republish, to post on servers or to redistribute to lists, requires prior specific permission and/or a fee. Request permissions from [email protected]

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Published: 05 May 1975

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Gruska J(2005)Descriptional complexity (of languages) a short surveyMathematical Foundations of Computer Science 197610.1007/3-540-07854-1_162(65-80)Online publication date: 21-May-2005
https://doi.org/10.1007/3-540-07854-1_162
Greibach S(1981)Formal LanguagesIEEE Annals of the History of Computing10.1109/MAHC.1981.100063:1(14-41)Online publication date: 1-Jan-1981
https://dl.acm.org/doi/10.1109/MAHC.1981.10006
Peterson G(1980)Succinct representation random strings, and complexity classesProceedings of the 21st Annual Symposium on Foundations of Computer Science10.1109/SFCS.1980.42(86-95)Online publication date: 13-Oct-1980
https://dl.acm.org/doi/10.1109/SFCS.1980.42
Greibach S(1979)Formal languagesProceedings of the 20th Annual Symposium on Foundations of Computer Science10.1109/SFCS.1979.19(66-90)Online publication date: 29-Oct-1979
https://dl.acm.org/doi/10.1109/SFCS.1979.19

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Context-free grammar forms

Tree insertion grammar: a cubic-time, parsable formalism that lexicalizes context-free grammar without changing the trees produced

Tree insertion grammar: a cubic-time, parsable formalism that lexicalizes context-free grammar without changing the trees produced

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Context-free grammar forms

Tree insertion grammar: a cubic-time, parsable formalism that lexicalizes context-free grammar without changing the trees produced

Tree insertion grammar: a cubic-time, parsable formalism that lexicalizes context-free grammar without changing the trees produced

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