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Approximating grammar probabilities: solution of a conjecture

Authors:

R. Chaudhuri,

A. N. V. RaoAuthors Info & Claims

Journal of the ACM (JACM), Volume 33, Issue 4

Pages 702 - 705

https://doi.org/10.1145/6490.214099

Published: 10 August 1986 Publication History

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Abstract

It is proved that the production probabilities of a probabilistic context-free grammar may be obtained as the limit of the estimates inferred from an increasing sequence of randomly drawn samples from the language generated by the grammar.

References

[1]

CHALIDHURi, R., AND RAO, A. N.V. On a property of probabilistic context-free grammars. Int. ~ Math. Math. Sci. 6, 2 (1983), 403-406.

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[2]

CHAUDHURI, R., PHAM, S., AND GARCIA, O. N. Solution of an open problem on probabilistic grammars. IEEE Trans. Comput. C-32, 8 (1983), 748-750.

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[3]

FELLER, W. Introduction to Probability Theory and Its Applications, vol. I. 3rd ed. Wiley, New York, 1968.

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HOPCROFT, J. E., AND ULLMAN, J. O. Formal Languages and Their Relation to Automata. Addison-Wesley, Reading, Mass., 1969.

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WETHERELL, C. S. Probabilistic languages: A review and some open questions. A CM Comput. Surv. 12, 4 (1980), 361-379.

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Cited By

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Infante-Lopez GRijke M(2006)A Note on the Expressive Power of Probabilistic Context Free GrammarsJournal of Logic, Language and Information10.1007/s10849-005-9002-x15:3(219-231)Online publication date: 1-Oct-2006
https://dl.acm.org/doi/10.1007/s10849-005-9002-x
Habrard ABernard MSebban M(2005)Detecting Irrelevant Subtrees to Improve Probabilistic Learning from Tree-structured DataFundamenta Informaticae10.5555/2370136.237014266:1-2(103-130)Online publication date: 1-Jan-2005
https://dl.acm.org/doi/10.5555/2370136.2370142
Vidal EThollard Fde la Higuera CCasacuberta FCarrasco R(2005)Probabilistic Finite-State Machines-Part IIIEEE Transactions on Pattern Analysis and Machine Intelligence10.1109/TPAMI.2005.14827:7(1026-1039)Online publication date: 1-Jul-2005
https://dl.acm.org/doi/10.1109/TPAMI.2005.148
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Index Terms

Approximating grammar probabilities: solution of a conjecture
1. Software and its engineering
  1. Software notations and tools
    1. Formal language definitions
2. Theory of computation
  1. Formal languages and automata theory
    1. Formalisms
      1. Rewrite systems
    2. Grammars and context-free languages

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Information

Published In

Journal of the ACM Volume 33, Issue 4

Oct. 1986

189 pages

ISSN:0004-5411

EISSN:1557-735X

DOI:10.1145/6490

Editor:
Daniel Rosencrantz

Issue’s Table of Contents

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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Association for Computing Machinery

New York, NY, United States

Publication History

Published: 10 August 1986

Published in JACM Volume 33, Issue 4

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Cited By

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Infante-Lopez GRijke M(2006)A Note on the Expressive Power of Probabilistic Context Free GrammarsJournal of Logic, Language and Information10.1007/s10849-005-9002-x15:3(219-231)Online publication date: 1-Oct-2006
https://dl.acm.org/doi/10.1007/s10849-005-9002-x
Habrard ABernard MSebban M(2005)Detecting Irrelevant Subtrees to Improve Probabilistic Learning from Tree-structured DataFundamenta Informaticae10.5555/2370136.237014266:1-2(103-130)Online publication date: 1-Jan-2005
https://dl.acm.org/doi/10.5555/2370136.2370142
Vidal EThollard Fde la Higuera CCasacuberta FCarrasco R(2005)Probabilistic Finite-State Machines-Part IIIEEE Transactions on Pattern Analysis and Machine Intelligence10.1109/TPAMI.2005.14827:7(1026-1039)Online publication date: 1-Jul-2005
https://dl.acm.org/doi/10.1109/TPAMI.2005.148
Dupont PDenis FEsposito Y(2005)Links between probabilistic automata and hidden Markov modelsPattern Recognition10.1016/j.patcog.2004.03.02038:9(1349-1371)Online publication date: 1-Sep-2005
https://dl.acm.org/doi/10.1016/j.patcog.2004.03.020
Varona ATorres I(2005)Scaling Smoothed Language ModelsInternational Journal of Speech Technology10.1007/s10772-006-9047-58:4(341-361)Online publication date: Dec-2005
https://doi.org/10.1007/s10772-006-9047-5
Habrard ABernard MSebban M(2004)Detecting Irrelevant Subtrees to Improve Probabilistic Learning from Tree-structured DataFundamenta Informaticae10.5555/1227174.122718066:1-2(103-130)Online publication date: 1-Nov-2004
https://dl.acm.org/doi/10.5555/1227174.1227180
Habrard ABernard MJacquenet F(2002)Generalized Stochastic Tree Automata for Multi-relational Data MiningProceedings of the 6th International Colloquium on Grammatical Inference: Algorithms and Applications10.5555/645519.655967(120-133)Online publication date: 23-Sep-2002
https://dl.acm.org/doi/10.5555/645519.655967
Habrard ABernard MJacquenet F(2002)Generalized Stochastic Tree Automata for Multi-relational Data MiningGrammatical Inference: Algorithms and Applications10.1007/3-540-45790-9_10(120-133)Online publication date: 5-Sep-2002
https://doi.org/10.1007/3-540-45790-9_10
Torres IVarona A(2001)k-TSS language models in speech recognition systemsComputer Speech and Language10.1006/csla.2001.016215:2(127-148)Online publication date: 1-Apr-2001
https://dl.acm.org/doi/10.1006/csla.2001.0162
Rico-Juan JCalera-Rubio JCarrasco R(2000)Probabilistic k-Testable Tree LanguagesGrammatical Inference: Algorithms and Applications10.1007/978-3-540-45257-7_18(221-228)Online publication date: 2000
https://doi.org/10.1007/978-3-540-45257-7_18
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Recommendations

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

Lfg generation by grammar specialization

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