Finite completion of comma-free codes. Part 2

Nguyen Huong Lam

RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications (2004)

  • Volume: 38, Issue: 2, page 117-136
  • ISSN: 0988-3754

Abstract

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This paper is a sequel to an earlier paper of the present author, in which it was proved that every finite comma-free code is embedded into a so-called (finite) canonical comma-free code. In this paper, it is proved that every (finite) canonical comma-free code is embedded into a finite maximal comma-free code, which thus achieves the conclusion that every finite comma-free code has finite completions.

How to cite

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Lam, Nguyen Huong. "Finite completion of comma-free codes. Part 2." RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications 38.2 (2004): 117-136. <http://eudml.org/doc/245676>.

@article{Lam2004,
abstract = {This paper is a sequel to an earlier paper of the present author, in which it was proved that every finite comma-free code is embedded into a so-called (finite) canonical comma-free code. In this paper, it is proved that every (finite) canonical comma-free code is embedded into a finite maximal comma-free code, which thus achieves the conclusion that every finite comma-free code has finite completions.},
author = {Lam, Nguyen Huong},
journal = {RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications},
keywords = {comma-free code; completion; finite maximal comma-free code},
language = {eng},
number = {2},
pages = {117-136},
publisher = {EDP-Sciences},
title = {Finite completion of comma-free codes. Part 2},
url = {http://eudml.org/doc/245676},
volume = {38},
year = {2004},
}

TY - JOUR
AU - Lam, Nguyen Huong
TI - Finite completion of comma-free codes. Part 2
JO - RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications
PY - 2004
PB - EDP-Sciences
VL - 38
IS - 2
SP - 117
EP - 136
AB - This paper is a sequel to an earlier paper of the present author, in which it was proved that every finite comma-free code is embedded into a so-called (finite) canonical comma-free code. In this paper, it is proved that every (finite) canonical comma-free code is embedded into a finite maximal comma-free code, which thus achieves the conclusion that every finite comma-free code has finite completions.
LA - eng
KW - comma-free code; completion; finite maximal comma-free code
UR - http://eudml.org/doc/245676
ER -

References

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  1. [1] J. Berstel and D. Perrin, Theory of Codes. Academic Press, Orlando (1985). Zbl0587.68066MR797069
  2. [2] N.J. Fine and H.S. Wilf, Uniqueness Theorem for Periodic Functions. Proc. Amer. Math. Soc. 16 (1965) 109-114. Zbl0131.30203MR174934
  3. [3] S.W. Golomb, B. Gordon and L.R. Welch, Comma-free Codes. Canad. J. Math. 10 (1958) 202-209. Zbl0081.14601MR95091
  4. [4] S.W. Golomb, L.R. Welch and M. Delbrück, Construction and Properties of Comma-free Codes. Biol. Medd. Dan. Vid. Selsk. 23 (1958) 3-34. 
  5. [5] M. Ito, M. Katsura, H.J. Shyr and S.S. Yu, Automata Accepting Primitive Words. Semigroup Forum 37 (1988) 45-52. Zbl0646.20055MR929442
  6. [6] M. Ito, H. Jürgensen, H.J. Shyr and G. Thierrin, Outfix and Infix Codes and Related Classes of Languages. J. Comput. Syst. Sci. 43 (1991) 484-508. Zbl0794.68087MR1135474
  7. [7] B.H. Jiggs, Recent Results in Comma-free Codes. Canad. J. Math. 15 (1963) 178-187. Zbl0108.14304MR143672
  8. [8] N.H. Lam, Finite Completion of Comma-Free Codes. Part 1, in Proc. of DLT 2002. Springer-Verlag, Lect. Notes Comput. Sci. 2450 357-368. Zbl1022.94005
  9. [9] R.C. Lyndon and M.-P. Shützenberger, The Equation a M = b N c P in a Free Group. Michigan Math. J. 9 (1962) 289-298. Zbl0106.02204MR162838
  10. [10] Al.A. Markov, An Example of an Independent System of Words Which Cannot Be Included in a Finite Complete System. Mat. Zametki 1 (1967) 87-90. Zbl0154.00703MR210594
  11. [11] A. Restivo, On Codes Having No Finite Completions. Discret Math. 17 (1977) 306-316. Zbl0357.94011MR498922
  12. [12] H.J. Shyr, Free Monoids and Languages. Lecture Notes, Hon Min Book Company, Taichung, 2001. Zbl0746.20050MR1090325
  13. [13] J.D. Watson and F.C.H. Crick, A Structure for Deoxyribose Nucleic Acid. Nature 171 (1953) 737. 

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