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On the complexity of grammar and related problems

Authors:

H. B. Hunt, III and

T. G. SzymanskiAuthors Info & Claims

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

May 1975

Pages 54 - 65

https://doi.org/10.1145/800116.803753

Published: 05 May 1975 Publication History

Abstract

In [1] and [2] a complexity theory for formal languages and automata was developed. This theory implies most of the previously known results and yields many new results as well. Here we develop an analogous theory for several classes of more practically motivated problems. Two such classes, both closely related to formal language and automata theory, suggest themselves - grammar problems and program scheme problems. Here, our primary emphasis is on grammar problems of interest in parsing and compiling. Other problems considered include -

(1) possible techniques for proving non-trivial lower complexity bounds for problems in P;

(2) the relationship of the complexity of tree automaton equivalence, structural equivalence, and grammatical covering; and

(3) the complexity of the equivalence problem for schemes.

In each case we relate the computational complexity of a problem to its underlying combinatorial structure. The remainder of the paper is divided into four sections.

References

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H. B. Hunt, III, On the time and tape complexity of languages, Ph.D. Thesis, Cornell University, Aug. 1973.

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W. F. Ogden, unpublished note (Dec. 1971).

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H. B. Hunt, III, T. G. Szymanski, and J. D. Ullman, On the complexity of LR(k) testing, Conf. Rec. 2nd ACM Symp. on Principles of Programming Languages (Jan. 1975), 130-136.

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H. B. Hunt, III, D. J. Rosenkrantz, and T. G. Szymanski, On the equivalence, containment, and covering problems for the regular and context-free languages (submitted for publication).

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Cited By

Price JWotschke D(2005)States can sometimes do more than stack symbols in PDA'sAutomata, Languages and Programming10.1007/3-540-08860-1_26(353-362)Online publication date: 26-May-2005
https://doi.org/10.1007/3-540-08860-1_26
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
(1989)BibliographyComputability, Complexity, Logic10.1016/S0049-237X(08)70326-4(528-573)Online publication date: 1989
https://doi.org/10.1016/S0049-237X(08)70326-4
Show More Cited By

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On the complexity of grammar and related problems

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cover image ACM Conferences

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

May 1975

265 pages

ISBN:9781450374194

DOI:10.1145/800116

Copyright © 1975 ACM.

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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STOC '75 Paper Acceptance Rate 31 of 87 submissions, 36%;

Overall Acceptance Rate 1,469 of 4,586 submissions, 32%

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Cited By

Price JWotschke D(2005)States can sometimes do more than stack symbols in PDA'sAutomata, Languages and Programming10.1007/3-540-08860-1_26(353-362)Online publication date: 26-May-2005
https://doi.org/10.1007/3-540-08860-1_26
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
(1989)BibliographyComputability, Complexity, Logic10.1016/S0049-237X(08)70326-4(528-573)Online publication date: 1989
https://doi.org/10.1016/S0049-237X(08)70326-4
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
Hunt HRosenkrantz DAbrahams PLipton RBourne S(1980)Efficient algorithms for structural similarity of grammarsProceedings of the 7th ACM SIGPLAN-SIGACT symposium on Principles of programming languages10.1145/567446.567467(213-219)Online publication date: 28-Jan-1980
https://dl.acm.org/doi/10.1145/567446.567467
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
Hunt HSzymanski TChandra AWotschke DFriedman EHarrison M(1976)Dichotomization, reachability, and the forbidden subgraph problem(Extended Abstract)Proceedings of the eighth annual ACM symposium on Theory of computing10.1145/800113.803640(126-134)Online publication date: 3-May-1976
https://dl.acm.org/doi/10.1145/800113.803640

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