Skip to main content

Automata and Computational Probabilities

  • Conference paper
  • First Online:
Automata Implementation (WIA 1998)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 1660))

Included in the following conference series:

  • 289 Accesses

Abstract

In this paper, we discuss the underlying ideas of a computer laboratory for symbolic manipulation of discrete random experiments. Finite automata, and associated formal series, are the basic theoretical tool for representing experiments, and for solving probability problems. Starting from a description of a random experiment given as a special kind of regular expressions, the environment constructs automata from which it extracts generating series associated to the experiment.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 39.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 54.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Aho, A., Hopcroft, J., Ullman, J., The Design and Analysis of Computer Algorithms, Addison-Wesley, 1974.

    Google Scholar 

  2. Beaulieu, M.C., Langages rationnels et probabilités discrétes, Mémoire de Maitrise, Université du Québec á Montréal, 1998.

    Google Scholar 

  3. Berstel, J., Perrin, D., Theory of Codes, Academic Press, 1985.

    Google Scholar 

  4. Berstel, J., Reutenauer, C., Les séries rationnelles et leurs langages, Masson, 1984.

    Google Scholar 

  5. Eilenberg, S., Automata, Languages and Machines, Vol A, Academic Press, 1974.

    Google Scholar 

  6. Flajolet, P., Salvy, B., Zimmermann, P., Automatic Average-Case Analysis of Algorithms, Theoretical Computer Science 79, 1991, 37–109.

    Article  MATH  MathSciNet  Google Scholar 

  7. Geniet, D., Thimonnier L., Using Generating Functions to Compute Concurrency, Fundamental of Computation Theory, LNCS 380, 1989, 185–196.

    Google Scholar 

  8. Hansel, G., Perrin, D., Rational Probability Measures, Theoretical Computer Science, 65, 1989, 171–188.

    Article  MATH  MathSciNet  Google Scholar 

  9. Penney, W., Problem 95: Penney-Ante, Journal of Recreational Mathematics, 7, 1974, 321.

    Google Scholar 

  10. Schtuzenberger, M. P., On the synchronizing properties of certain prefix codes, Inform. and Control 7, 1964, 23–36.

    Article  Google Scholar 

  11. Shannon, C., The Mathematical Theory of Communication, The University of Illinois Press, Urbana, 1949.

    MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 1999 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Beaulieu, MC., Bergeron, A. (1999). Automata and Computational Probabilities. In: Champarnaud, JM., Ziadi, D., Maurel, D. (eds) Automata Implementation. WIA 1998. Lecture Notes in Computer Science, vol 1660. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-48057-9_14

Download citation

  • DOI: https://doi.org/10.1007/3-540-48057-9_14

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-66652-3

  • Online ISBN: 978-3-540-48057-0

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics