research-article

Language Correction Using Probabilistic Grammars

Author:

Richard A. ThompsonAuthors Info & Claims

IEEE Transactions on Computers, Volume 25, Issue 3

Pages 275 - 286

https://doi.org/10.1109/TC.1976.5009254

Published: 01 March 1976 Publication History

Abstract

Error correction of programming languages has been effected in a heuristic fashion; error correction in the information-theoretic sense is very precise. The missing link is provided through probabilistic grammars. This paper provides the theoretical foundation for the precise construction of an error correcting compiler. The concept of code distance is extended to account for syntax in language. Grammar modifications are demonstrated so that a probabilistic parsing algorithm corrects various kinds of linguistic errors using an ideal observer rule. A generalized error correcting algorithm is described.

References

[1]

A. V. Aho and T. G. Peterson, "A minimum distance error correcting paarser for context-free languages," SIAM J. Comput., Dec. 1972.

[2]

A. V. Aho and J. D. Ullman, The Theory of Parsing, Translation, and Compiling. Englewood Cliffs, NJ: Prentice-Hall, 1972.

Digital Library

[3]

T. L. Booth, "Probabilistic representation of formal languages," in Conf. Rec. IEEE Symp. Switching and Automata Theory, 1969.

[4]

R. L. Booth and R. A. Thompson, "Applying probability measures to abstract languages," IEEE Trans. Comput., vol. C-22, pp. 442-450, May 1973.

[5]

F. J. Damerau, "A technique for computer detection and correction of spelling errors," Commun. Ass. Comput. Mach., Mar. 1964.

[6]

C. A. Ellis, "Probabilistic languages and automatil," Ph.D. diRsertation, Univ. Illinois, Urbana, 1969.

[7]

K. S. Fu, Syntactic Methods in Pattern Recognition. New York: Academic, 1974.

[8]

L. W. Fung and K. S. Fu, "Communication of languages using syntactic information," in Proc. IEEE Int. Symp. Tnform. Theory, 1974.

[9]

L. W. Fung and K. S. Fu, "Maximum likelihood syntactic decoding," IEEE Trans. Inform. Theory, vol. IT-21, pp. 423-430, July 1975.

[10]

L. W. Fung and K. S. Fu, "Stochastic syntactic decoding for pattern classification," IEEE Trans. Comput., vol. C-24, pp. 662-667, June 1975.

[11]

J. E. Hopcroft and J. D. Ullman, "Error correclion for formal languages," Digital Syst. Lab., Princeton, Univ., Princeton, NJ, Tech. Rep. 52, Nov. 1966.

[12]

J. E. Hopcroft and J. D. Ullman, Formal Languages and Their Relation to Automata. Reading, MA: Addison-Wesley, 1969.

Digital Library

[13]

S. E. Hutchins, "Data compression in context-free languages," in Proc. Int. Fed. Inform. Processing, 1971.

[14]

E. T. Irons, "An error-correcting parse algorithm," Commun. Ass. Comput. Mach., Nov. 1963.

[15]

V. A. Kovalevsky, "Sequential optimization in pattern recognition and pattern description," in Proc. Int. Fed. Inform. Processing Soc., 1968.

[16]

H. C. Lee and K. S. Fu, "A stochastic syntax analysis procedure and its application to pattern classification," IEEE Trans. Comput. (Special Issue on Two-Dimensional Signal Processing), vol. C-21, pp. 660-666, July 1972.

[17]

G. Lyon, "Syntax-directed least-errors analysis for context-free languages: A practical approach," Commun. Ass. Comput. Mach., Jan. 1974.

[18]

H. L. Morgan, "Spelling correction in systems programs," Commun. Ass. Comput. Mach., Feb. 1970.

[19]

W. B. Smith, "Error detection in formal languages," J. Comput. Syst. Sci., Apr. 1970.

[20]

M. G. Thomason, "Errors in regular languages," IEEE Trans. Comput., vol. C-23, pp. 597-602, June 1974.

[21]

R. A. Thompson, "Compact encoding of probabilistic languages," Ph.D. dissertation, Univ. Connecticut, Storrs, 1971.

Digital Library

[22]

R. A. Thompson and T. L. Booth, "Encoding of probabilistic context-free languages," in Theory of Machines and Computations, Z. Kohavi and A. Paz, Eds. New York: Academic, 1971.

[23]

R. A. Thompson, "Determination of probabilistic grammars for functionally specified probability measure languages," IEEE Trans. Comput., vol. C-23, pp. 603-614, June 1974.

[24]

R. A. Wagner and M. J. Fischer, "The string-to-string correction problem," J. Ass. Comput. Mach., Jan. 1974.

[25]

R. A. Wagner, "Order-n correction for regular languages," Commun. Ass. Comput. Mach., May 1974.

Cited By

Sakkas GEndres MGuo PWeimer WJhala R(2022)Seq2Parse: neurosymbolic parse error repairProceedings of the ACM on Programming Languages10.1145/35633306:OOPSLA2(1180-1206)Online publication date: 31-Oct-2022
https://dl.acm.org/doi/10.1145/3563330
Wu LLi FWu YZheng T(2020)GGFProceedings of the 28th International Conference on Program Comprehension10.1145/3387904.3389252(139-148)Online publication date: 13-Jul-2020
https://dl.acm.org/doi/10.1145/3387904.3389252
Shin-Yee Lu King-Sun Fu (1977)Stochastic Error-Correcting Syntax Analysis for Recognition of Noisy PatternsIEEE Transactions on Computers10.1109/TC.1977.167478826:12(1268-1276)Online publication date: 1-Dec-1977
https://dl.acm.org/doi/10.1109/TC.1977.1674788
Show More Cited By

Language Correction Using Probabilistic Grammars
1. Theory of computation
  1. Formal languages and automata theory

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cover image IEEE Transactions on Computers

IEEE Transactions on Computers Volume 25, Issue 3

March 1976

110 pages

ISSN:0018-9340

Issue’s Table of Contents

Copyright © 1976.

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IEEE Computer Society

United States

Publication History

Published: 01 March 1976

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Cited By

Sakkas GEndres MGuo PWeimer WJhala R(2022)Seq2Parse: neurosymbolic parse error repairProceedings of the ACM on Programming Languages10.1145/35633306:OOPSLA2(1180-1206)Online publication date: 31-Oct-2022
https://dl.acm.org/doi/10.1145/3563330
Wu LLi FWu YZheng T(2020)GGFProceedings of the 28th International Conference on Program Comprehension10.1145/3387904.3389252(139-148)Online publication date: 13-Jul-2020
https://dl.acm.org/doi/10.1145/3387904.3389252
Shin-Yee Lu King-Sun Fu (1977)Stochastic Error-Correcting Syntax Analysis for Recognition of Noisy PatternsIEEE Transactions on Computers10.1109/TC.1977.167478826:12(1268-1276)Online publication date: 1-Dec-1977
https://dl.acm.org/doi/10.1109/TC.1977.1674788
King-Sun Fu Rosenfeld A(1976)Pattern Recognition and Image ProcessingIEEE Transactions on Computers10.1109/TC.1976.167460225:12(1336-1346)Online publication date: 1-Dec-1976
https://dl.acm.org/doi/10.1109/TC.1976.1674602

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