Skip to main content
SpringerLink
Log in

Symbolic dynamics and finite automata

  • Invited Papers
  • Conference paper
  • First Online:
Mathematical Foundations of Computer Science 1995 (MFCS 1995)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 969))

Abstract

In this survey, we present some connections between notions and results in automata theory and other ones in symbolic dynamics.

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

Access this chapter

Log in via an institution

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Roy Adler, I. Goodwin, and Benjamin Weiss. Equivalence of topological Markov shifts. Israel J. Math., 27:49–63, 1977.

    Google Scholar 

  2. John Ashley, Brian Marcus, Dominique Perrin, and Selim Tuncel. Surjective extensions of sliding block codes. SIAM J. Discrete Math., 6:582–611, 1993.

    Article  Google Scholar 

  3. Frédérique Bassino. Hauteur d'étoile d'une série IN-rationnelle. Technical report, Institut Gaspard Monge, 1995.

    Google Scholar 

  4. Marie-Pierre Béal. Codage Symbolique. Masson, 1993.

    Google Scholar 

  5. Marie-Pierre Béal and Olivier Carton. Cyclic languages and languages of stabilizers. Technical report, Institut Gaspard Monge, 1995.

    Google Scholar 

  6. Danièle Beauquier. Minimal automaton for a factorial, transitive rational language. Theoret Comput. Sci., 67:65–73, 1989.

    Google Scholar 

  7. Tim Bedford, Michael Keane, and Caroline Series, editors. Ergodic Theory, Symbolic Dynamics and Hyperbolic Spaces. Oxford University Press, 1991.

    Google Scholar 

  8. Jean Berstel and Dominique Perrin. Theory of codes. Academic Press, 1985.

    Google Scholar 

  9. Jean Berstel and Christophe Reutenauer. Zeta functions of formal languages. Trans. Amer. Math. Soc., 321:533–546, 1990.

    Google Scholar 

  10. François Blanchard and Georges Hansel. Languages and subshifts. In M. Nivat and D. Perrin, editors, Automata on Infinite Words, volume 192 of Lecture notes in Computer Science, pages 138–146. Springer Verlag, 1985.

    Google Scholar 

  11. François Blanchard and Alejandro Maass. On dynamical properties of generalized cellular automata. In Ricardo Baeeza-Yates and Eric Goles, editors, LATIN 95: Theoretical Informatics, volume 911 of Lecture Notes in Comput. Sci., pages 84–98, 1995.

    Google Scholar 

  12. Rufus Bowen and O. Lanford. Zeta functions of restrictions of the shift transformation. Proc. Symp. Pure Math., 14:43–50, ?

    Google Scholar 

  13. Mike Boyle. Symbolic dynamics and matrices. In S Friedland, V. Brualdi, and V. Klee, editors, Combinatorial and Graph-Theoretic Problems in Linear Algebra, volume 50 of IMA Volumes in Mathematics and its Applications. 1993.

    Google Scholar 

  14. Véronique Bruyère, L. Wong, and Liang Zhang. On completion of codes with finite deciphering delay. European J. Combin., 11:513–521, 1990.

    Google Scholar 

  15. Christian Choffrut. Conjugacy in free inverse monoids. Int. J. Alg. Comput., 3:169–188, 1993.

    Google Scholar 

  16. R. Fischer. Sofic systems and graphs. Monatshefte Math., 80:179–186, 1975.

    Google Scholar 

  17. Christiane Frougny and Boris Solomyak. Finite beta-expansions. Ergod. Th. & Dynam. Syst., 12:45–82, 1992.

    Google Scholar 

  18. David Handelman. Positive matrices and dimension groups affiliated to C *- algebras and topological Markov chains. J. Operator Theory, 6:55–74, 1981.

    Google Scholar 

  19. David Handelman. Spectral radii of primitive integral companion matrices and log-concave poynomials. In Peter Walters, editor, Symbolic Dynamics and its Applications, volume 135 of Contemporary Mathematics, pages 231–238. Amer. Math. Soc., 1992.

    Google Scholar 

  20. K. H. Kim and F. W. Roush. Decidability of shift equivalence. In Symbolic Dynamics, volume 1342 of Lecture Notes in Mathematics, pages 374–424. Springer, 1988.

    Google Scholar 

  21. K. H. Kim and F. W. Roush. William's conjecture is false for reducible matrices. J. Amer. Math. Soc., 5:213–215, 1992.

    Google Scholar 

  22. Wolfgang Krieger. On the subsystems of topological Markov chains. Ergod. Th. & Dynam. Syst., 2:195–202, 1982.

    Google Scholar 

  23. Anthony Manning. Axiom a diffeomorphisms have rational zeta function. Bull. London Math. Soc., 3:215–220, 1971.

    Google Scholar 

  24. M. Morse and G. Hedlund. Symbolic dynamics. Amer. J. of Math., 3:286–303, 1936.

    Google Scholar 

  25. Marston Morse. Recurrent geodesics on a surface of negative curvature. Trans. Amer. Math. Soc., 22:84–110, 1921.

    MathSciNet  Google Scholar 

  26. Dominique Perrin. Arbres et séries rationnelles. C. R. Acad. Sci. Paris, 309:713–716, 1989.

    Google Scholar 

  27. Dominique Perrin and Marcel-Paul Schützenberger. Synchronizing prefix codes and automata and the road coloring problem. In Peter Walters, editor, Symbolic Dynamics and its Applications, volume 135 of Contemporary Mathematics, pages 295–318. Amer. Math. Soc., 1992.

    Google Scholar 

  28. Antonio Restivo. Codes and local constraints. Theoret. Comput. Sci., 72:55–64, 1990.

    Google Scholar 

  29. Christophe Reutenauer. Non commutative factorization of variable length codes. J. Pure and Applied Algebra, 36:157–186, 1985.

    Google Scholar 

  30. A. Salomaa and Matti Soittola. Automatic-Theoretic Aspects of Formal Power Series. New York, Springer-Verlag, 1978.

    Google Scholar 

  31. Marcel-Paul Schützenberger. On synchronizing prefix codes. Inform and Control, 11:396–401, 1967.

    Google Scholar 

  32. Peter Walters, editor. Symbolic Dynamics and its Applications, volume 135 of Contemporary Mathematics. Amer. Math. Soc., 1992.

    Google Scholar 

  33. Benjamin Weiss. Subshifts of finite type and sofic systems. Monats. Math., 77:462–474, 1973.

    Google Scholar 

  34. Frank Williams. Classification of subshifts of finite type. Ann. of Math., 98:120–153, 1973. (Errata ibid. 99:380–381,1974).

    Google Scholar 

  35. Liang Zhang and Zhonghui Shen. Completion of recognizable bifix codes. Theoret. Comput. Sci., 145:345–355, 1995.

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Université de Marne la Vallée, 93166, Noisy le Grand, France

    Dominique Perrin

Authors
  1. Dominique Perrin
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Jiří Wiedermann Petr Hájek

Rights and permissions

Reprints and permissions

Copyright information

© 1995 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Perrin, D. (1995). Symbolic dynamics and finite automata. In: Wiedermann, J., Hájek, P. (eds) Mathematical Foundations of Computer Science 1995. MFCS 1995. Lecture Notes in Computer Science, vol 969. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-60246-1_116

Download citation

  • DOI: https://doi.org/10.1007/3-540-60246-1_116

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-60246-0

  • Online ISBN: 978-3-540-44768-9

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics

Search

Navigation