Skip to main content
SpringerLink
Log in

Variable-length maximal codes

  • Invited Papers
  • Conference paper
  • First Online:
Automata, Languages and Programming (ICALP 1996)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 1099))

Included in the following conference series:

Abstract

In this survey, we present some of the main open problems in the theory of variable-length codes, together with the major advancements recently realized to solve them.

This work was partially supported by a cooperation project CGRI-FNRS-CNRS.

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. J. Ashley, B. Marcus, D. Perrin, S. Tuncel, Surjective extensions of sliding block codes, SIAM J. Discrete Math. 6 (1993) 582–611.

    Article  Google Scholar 

  2. J. Berstel, D. Perrin, Theory of Codes, Academic Press (1985).

    Google Scholar 

  3. J. Berstel, D. Perrin, Trends in the theory of codes, Bull. EATCS 29 (1986) 84–95.

    Google Scholar 

  4. J. Berstel, C. Reutenauer, Rational series and their languages, EATCS Monogr. Theoret. Comput. Sci. 12, Springer-Verlag (1988).

    Google Scholar 

  5. J.-M. Boë, Une famille remarquable de codes indécomposables, Lecture Notes in Comput. Sci. 62 (1978) 105–112.

    Google Scholar 

  6. J.-M. Boë, Sur les codes synchronisants coupants, in: Non-commutative Structures in Algebra and Geometric Combinatorics, A. De Luca, Ed., Quaderni de la Ricerca Scientifica 109 (1981) 7–10.

    Google Scholar 

  7. J.-M. Boë, Factorisation par excès du monoïde libre, Technical Report 94-005, University of Montpellier (1994) 6 pages.

    Google Scholar 

  8. V. Bruyère, Automata and codes with bounded deciphering delay, Lecture Notes in Comput. Sci. 583 (1992) 99–107.

    Google Scholar 

  9. V. Bruyère, D. Derencourt, M. Latteux, The meet operation in the lattice of codes submitted (1996) 16 pages.

    Google Scholar 

  10. V. Bruyère, L. Wang, L. Zhang, On completion of codes with finite deciphering delay, European J. Combin. 11 (1990) 513–521.

    Google Scholar 

  11. J. Brzozowski, Open problems about regular languages, in: Formal Language Theory: Perspectives and Open Problems, R.V. Book, Ed., Academic Press (1980) 23–45.

    Google Scholar 

  12. A. Carpi, On synchronizing unambiguous automata, Theoret. Comput. Sci. 60 (1988) 285–296.

    Article  Google Scholar 

  13. Y. Césari, Sur l'application du théorème de Suschkevitch à l'étude des codes rationnels complets, in: Automata, Languages and Programming, Lecture Notes in Comput. Sci. (1974) 342–350.

    Google Scholar 

  14. N. G. de Bruijn, On the factorization of cyclic groups, Indag. Math. 15 (1953) 258–264.

    Google Scholar 

  15. D. Derencourt, A three-word code which is not prefix-suffix composed, to appear in Theoret. Comput. Sci (1996) 15 pages.

    Google Scholar 

  16. D. Derencourt, personal communication (1996).

    Google Scholar 

  17. C. De Felice, A partial result about the factorization conjecture for finite variable-length codes, Discrete Math. 122 (1993) 137–152.

    Article  Google Scholar 

  18. C. De Felice, An application of Hajós factorizations to variable-length codes, to appear in Theoret. Comput. Sci. (1996) 31 pages.

    Google Scholar 

  19. C. De Felice, A. Restivo, Some results on finite maximal codes, RAIRO Inform. Théor. Appl. 19 (1985) 383–403.

    Google Scholar 

  20. C. De Felice, C. Reutenauer, Solution partielle de la conjecture de factorisation des codes C. R. Acad. Sci. Paris 302 (1986) 169–170.

    Google Scholar 

  21. A. Ehrenfeucht, G. Rozenberg, Each regular code is included in a regular maximal code, RAIRO Inform. Théor. Appl. 20 (1985) 89–96.

    Google Scholar 

  22. S. Eilenberg, Automata, Languages and Machines, Vol. A, Academic Press (1974).

    Google Scholar 

  23. L. Fuchs, Abelian Groups, Pergamon Press (1960).

    Google Scholar 

  24. G. Hajós, Sur la factorisation des groupes abéliens, Casopis Pest. Mat. Fys. 74 (1950) 157–162.

    Google Scholar 

  25. R.W. Hamming, Coding and Information Theory, Prentice-Hall (1986).

    Google Scholar 

  26. J. Hopcroft, J. Ullman, Introduction to Automata Theory, Languages and Computation, Addison-Wesley (1979).

    Google Scholar 

  27. H. Jürgensen, S. Konstantinidis, Codes, in: Handbook of Formal Languages, G. Rozenberg, A. Salomaa, Eds, Springer-Verlag, to appear (1996).

    Google Scholar 

  28. R. König, Lectures on codes, Technical Report 93-3, University of Erlangen (1993) 66 pages.

    Google Scholar 

  29. M. Krasner, B. Ranulac, Sur une propriété des polynômes de la division du cercle, C. R. Acad. Sci. Paris 240 (1937) 397–399.

    Google Scholar 

  30. N. H. Lam, On codes having no finite completion, Lecture Notes in Comput. Sci. 775 (1994) 691–698.

    Google Scholar 

  31. N.H. Lam, A property of finite maximal codes, preprint (1996) 8 pages.

    Google Scholar 

  32. D. Lind, B. Marcus, Symbolic Dynamics and Coding, Cambridge University Press (1996).

    Google Scholar 

  33. A. A. Markov, An example of an independent system of words which cannot be included in a finite complete system (in Russian), Mat. Zametki 1 (1967) 87–90.

    Google Scholar 

  34. R.J. McEliece, The Theory of Information and Coding, Enc. of Math. 3, Addison-Wesley (1977).

    Google Scholar 

  35. F.J. McWilliams, N.J.A. Sloane, The Theory of Error-Correcting Codes, North-Holland (1977).

    Google Scholar 

  36. R. Montalbano, Local automata and completion, Lecture Notes in Comput. Sci. 665 (1993) 333–342.

    Google Scholar 

  37. D. Perrin, Completing biprefix codes, Theoret. Comput. Sci. 28 (1984) 329–336.

    Article  Google Scholar 

  38. D. Perrin, Finite automata, in: Handbook of Theoretical Computer Science, vol. B, J. Van Leeuwen, Ed., Elsevier (1990) 2–57.

    Google Scholar 

  39. D. Perrin, M.-P. Schützenberger, Un problème élémentaire de la théorie de l'information, Théorie de l'Information, Colloques Internat. CNRS 276, Cachan (1977) 249–260.

    Google Scholar 

  40. A. Restivo, On codes having no finite completions, Discrete Math. 17 (1977) 309–316.

    Article  Google Scholar 

  41. A. Restivo, S. Salemi, T. Sportelli, Completing codes, RAIRO Inform. Théor. Appl. 23 (1989) 135–147.

    Google Scholar 

  42. C. Reutenauer, Non commutative factorization of variable length codes, J. Pure Appl. Algebra 36 (1985) 157–186.

    Article  Google Scholar 

  43. A. Salomaa, Jewels of Formal Language Theory, Washington, D.C.: Computer Science Press (1981).

    Google Scholar 

  44. A. D. Sands, On a conjecture og G. Hajós, Glasgow Math. J. 15 (1974) 88–89.

    Google Scholar 

  45. M.-P. Schützenberger, Une théorie algébrique du codage, Séminaire Dubreil-Pisot 1955–56, exposé no 15 (1955).

    Google Scholar 

  46. M.-P. Schützenberger, Sur certains sous-monoïdes libres, Bull. Soc. Math. France 93 (1965) 209–223.

    Google Scholar 

  47. M.-P. Schützenberger, On a question concerning certain free submonoids, J. Combin. Theory 1 (1966) 437–442.

    Google Scholar 

  48. P. Shor, A counterexample to the triangle conjecture, J. Combin. Theor. Ser. A 38 (1983) 110–112.

    Article  Google Scholar 

  49. H.J. Shyr, Free Monoids and Languages, Hon Min Book Company, Taichung, second ed. (1991).

    Google Scholar 

  50. S. Szabo, personal communication to A. Restivo (1992).

    Google Scholar 

  51. J.H. Van Lindt, Introduction to Coding Theory, Graduate Texts in Math. 86, Springer-Verlag (1982).

    Google Scholar 

  52. L. Zhang, Every finite maximal code is a factorizing code, manuscript (1993) 19 pages.

    Google Scholar 

  53. L. Zhang, C.K. Gu, Two classes of factorizing codes — (p,p) codes and (4, 4) codes, In: Words, languages and combinatorics II, M. Ito, H. Jürgensen, Eds., World Scientific (1994) 477–483.

    Google Scholar 

  54. L. Zhang, Z. Shen, Completion of recognizable bifix codes, Theoret. Comput. Sci. 145 (1995) 345–355.

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. University of Mons-Hainaut, 15 Avenue Maistriau, B-7000, Mons, Belgium

    Véronique Bruyère

  2. University of Lille, L.I.F.L., Bâtiment M3, F-59655, Villeneuve d'Ascq, France

    Michel Latteux

Authors
  1. Véronique Bruyère
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Michel Latteux
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Friedhelm Meyer Burkhard Monien

Rights and permissions

Reprints and permissions

Copyright information

© 1996 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Bruyère, V., Latteux, M. (1996). Variable-length maximal codes. In: Meyer, F., Monien, B. (eds) Automata, Languages and Programming. ICALP 1996. Lecture Notes in Computer Science, vol 1099. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-61440-0_115

Download citation

  • DOI: https://doi.org/10.1007/3-540-61440-0_115

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-61440-1

  • Online ISBN: 978-3-540-68580-7

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics

Search

Navigation