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International Symposium on Fundamentals of Computation Theory

FCT 1993: Fundamentals of Computation Theory pp 352–362Cite as

Regular approximations to shuffle products of context-free languages, and convergence of their generating functions

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Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 710))

Abstract

We approximate certain languages, obtained as shuffle products of Dyck languages, by regular languages. These regular approximants are obtained by restricting the automaton accepting the original language to a finite maximum amount of storage, N. We study the dominant singularities of the multivariate generating functions of the approximants. By using formal asymptotic methods drawn from applied probability to work out the N → ∞ asymptotics of these singularities, we quantify the rate at which the approximants approach the original languages.

Supported in part by the U.S. National Science Foundation under grant NCR-9016211.

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References

  1. J. Berstel and C. Reutenauer. Rational Series and Their Languages. Springer-Verlag, 1988.

    Google Scholar 

  2. P. Flajolet. The evolution of two stacks in bounded space and random walks in a triangle. In Proceedings of MFCS '86, LNCS #244. Springer-Verlag, 1986.

    Google Scholar 

  3. P. Flajolet. Analytic models and ambiguity of context-free languages. Theoret. Comput. Sci. 49 (1987), 283–309.

    Article  Google Scholar 

  4. M. Fliess. Sur divers produits de séries formelles. Bull. Soc. Math. France 102 (1974), 181–191.

    Google Scholar 

  5. D. Geniet, R. Schott, and L. Thimonier. A Markovian concurrency measure. In Proceedings of CAAP '90, LNCS #431. Springer-Verlag, 1990.

    Google Scholar 

  6. C. Knessl, B. J. Matkowsky, Z. Schuss, and C. Tier. An asymptotic theory of large deviations for Markov jump processes. SIAM J. Appl. Math. 46 (1985), 1006–1028.

    Article  Google Scholar 

  7. G. Louchard and R. Schott. Probabilistic analysis of some distributed algorithms. Random Structures and Algorithms 2 (1991), 151–186. A preliminary version appeared in Proceedings of CAAP '90, LNCS #431. Springer-Verlag, 1990.

    Google Scholar 

  8. R. S. Maier. Colliding stacks: a large deviations analysis. Random Structures and Algorithms 2 (1991), 379–420.

    Google Scholar 

  9. R. S. Maier. Communications networks as stochastically perturbed nonlinear systems: A cautionary note. In Proceedings of the 30th Allerton Conference on Communication, Control and Computing (Monticello, Illinois, 1992), pp. 674–681.

    Google Scholar 

  10. R. S. Maier and C. A. O'Cinneide. A closure characterization of phase-type distributions. J. Appl. Probab. 29 (1992), 92–103.

    Google Scholar 

  11. T. Naeh, M. M. Klosek, B. J. Matkowsky, and Z. Schuss. A direct approach to the exit problem. SIAM J. Appl. Math. 50 (1990), 595–627.

    Article  Google Scholar 

  12. A. Salomaa and M. Soittola. Automata-Theoretic Aspects of Formal Power Series. Springer-Verlag, 1978.

    Google Scholar 

  13. E. Seneta. Non-negative Matrices and Markov Chains. Springer-Verlag, second edition, 1981.

    Google Scholar 

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Author information

Authors and Affiliations

  1. Dept. of Mathematics, University of Arizona, 85721, Tucson, Arizona, USA

    Robert S. Maier

  2. Université Nancy 1, C.R.I.N. and INRIA-Lorraine, 54506, Vandœuvre-lès-Nancy, France

    René Schott

Authors
  1. Robert S. Maier
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  2. René Schott
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Editor information

Zoltán Ésik

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© 1993 Springer-Verlag Berlin Heidelberg

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Maier, R.S., Schott, R. (1993). Regular approximations to shuffle products of context-free languages, and convergence of their generating functions. In: Ésik, Z. (eds) Fundamentals of Computation Theory. FCT 1993. Lecture Notes in Computer Science, vol 710. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-57163-9_30

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  • DOI: https://doi.org/10.1007/3-540-57163-9_30

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-57163-6

  • Online ISBN: 978-3-540-47923-9

  • eBook Packages: Springer Book Archive

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