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On formal languages, probabilities, paging and decoding algorithms

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Fundamentals of Computation Theory (FCT 1985)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 199))

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Abstract

In previous papers [BT 83] [BT 84] [BT 85], it was indicated how a probabilistic parameter, namely the Bernoullian density, could be computed by means of an explicit formula or numerically with a given precision for several structural types of formal Languages L. We present here two general methods for this computing, a deterministic one and a Monte-Carlo method, using the generating function of the prefix-free language Pref(L) associated with L, and a recognition algorithm for Pref(L) assumed to be context-free. The results are applied for the obtainment of new algorithms for two classical problems : paging and decoding, within a probabilistic framework of language theory.

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References

  1. J. BEAUQUIER —"Prefix and perfect languages"— Proceedings of the 8th C.A.A.P. (Italy 1983)— Lecture Notes in Computer Science 159, pp 129–140

    Google Scholar 

  2. J. BERSTEL —"Transductions and context-free languages"— Teubner Verlag (1979)

    Google Scholar 

  3. J.R. BUNCH, J.E. HOPCROFT —Math. Comp. 28 (1974) pp 231–236

    Google Scholar 

  4. L.R. BAHL, F. JELINEK —"Decoding for channels with insertions, deletions, and substitutions with applications to speech recognition"— I.E.E.E. transactions on information theory —Vol IT21 no4 pp 404–411 July 1975

    Google Scholar 

  5. J. BEAUQUIER, L. THIMONIER —"Formal languages and Bernoulli processes"— to appear in "Algebra, Combinatorics and Logic in Computer science", Colloquia Mathematica Soc. J. Bolyai (Hungary 1983), vol 42, North Holland

    Google Scholar 

  6. J. BEAUQUIER, L. THIMONIER —"Computability of probabilistic parameters for some classes of formal languages"— Proceedings of the 11th M.F.C.S. (Czechoslovakia 1984) —Lecture Notes in Computer Science 176, pp194–204.

    Google Scholar 

  7. J. BEAUQUIER, L. THIMONIER —"Prefix-free words of length n over m letters: two-sided well-balanced parentheses, and palindroms"— Proceedings of the "Colloque de Combinatoire Enumérative", UQAM 1985, Montréal (Canada)— to appear in Lecture Notes in Mathematics

    Google Scholar 

  8. F.G. COFFMAN, P.J. DENNING —"Operating system theory"— Prentice Hall Englewood Cliffs, N.J. (1973)

    Google Scholar 

  9. K.L. CHUNG —"Elementary probability theory with stochastic processes"— Springer Verlag (1979)

    Google Scholar 

  10. N. CHOMSKY, M.P. SCHUTZENBERGER—" The algebraic theory of context-free languages"— Computer Programming and Formal systems pp 118–161 North Holland (1963)

    Google Scholar 

  11. S. EILENBERG —"Automata, languages, and machines"— Vol. A. Academic Press (1974)

    Google Scholar 

  12. P. FLAJOLET —"Ambiguity and transcendence"-Proceedings of the 12th ICALP (Greece 1985)—To appear in lecture Notes in Computer science

    Google Scholar 

  13. E.B. FERNANDEZ, T. LANG, C. WOOD —"Minimization of demand paging for the LRU stack model of program"— Information proceedings letters 16 (1983), pp 99–104

    Google Scholar 

  14. J. GOLDSTINE —"Substitution and bounded languages"— Journal of Computer and System Sciences 6 (1972) pp 9–29

    Google Scholar 

  15. M. HARRISON —"Introduction to formal languages theory"— Addison Wesley (1978)

    Google Scholar 

  16. J.M. HAMMERSLEY, D.C. HANDSCOMB —"Monte-Carlo Methods"— London: Methuen (1964)

    Google Scholar 

  17. R.A. HOWARD —"Dynamic programming and Markov processes "— John Wiley, New-York (1960)

    Google Scholar 

  18. R. SEDGEWICK —"Mathematical Analysis of Combinatorial Algorithms "— In G. Louchard, G. Latouche ed., Probabilistic theory and Computer Science, Acad. Press (1983)

    Google Scholar 

  19. A. SEIDENBERG —"Elements of the theory of algebraic curves"— Addison Wesley (1965)

    Google Scholar 

  20. J.R. SPIRN —" Program Behavior: Models and Measurements"— North Holland (1977)

    Google Scholar 

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Author information

Authors and Affiliations

  1. Laboratoire de Recherche en Informatique (LRI), Université de Paris-SUD Bâtiment, 490 - 91 405, Orsay Cédex, France

    Joffroy Beauquier & Loÿs Thimonier

  2. U.E.R. de Mathématiques, Université d'Amiens, 33 rue St Leu, 80039, Amiens Cédex, France

    Loÿs Thimonier

Authors
  1. Joffroy Beauquier
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  2. Loÿs Thimonier
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Editor information

Lothar Budach

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© 1985 Springer-Verlag Berlin Heidelberg

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Beauquier, J., Thimonier, L. (1985). On formal languages, probabilities, paging and decoding algorithms. In: Budach, L. (eds) Fundamentals of Computation Theory. FCT 1985. Lecture Notes in Computer Science, vol 199. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0028790

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  • DOI: https://doi.org/10.1007/BFb0028790

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-15689-5

  • Online ISBN: 978-3-540-39636-9

  • eBook Packages: Springer Book Archive

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