Finite Completion of comma-free codes Part 2

Nguyen Huong Lam

RAIRO - Theoretical Informatics and Applications (2010)

  • 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 38.2 (2010): 117-136. <http://eudml.org/doc/92735>.

@article{Lam2010,
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},
keywords = {Comma-free code; completion; finite maximal comma-free code.},
language = {eng},
month = {3},
number = {2},
pages = {117-136},
publisher = {EDP Sciences},
title = {Finite Completion of comma-free codes Part 2},
url = {http://eudml.org/doc/92735},
volume = {38},
year = {2010},
}

TY - JOUR
AU - Lam, Nguyen Huong
TI - Finite Completion of comma-free codes Part 2
JO - RAIRO - Theoretical Informatics and Applications
DA - 2010/3//
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/92735
ER -

References

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  1. J. Berstel and D. Perrin, Theory of Codes. Academic Press, Orlando (1985).  Zbl0587.68066
  2. N.J. Fine and H.S. Wilf, Uniqueness Theorem for Periodic Functions. Proc. Amer. Math. Soc.16 (1965) 109-114.  Zbl0131.30203
  3. S.W. Golomb, B. Gordon and L.R. Welch, Comma-free Codes. Canad. J. Math.10 (1958) 202-209.  Zbl0081.14601
  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. M. Ito, M. Katsura, H.J. Shyr and S.S. Yu, Automata Accepting Primitive Words. Semigroup Forum37 (1988) 45-52.  Zbl0646.20055
  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.  Zbl0794.68087
  7. B.H. Jiggs, Recent Results in Comma-free Codes. Canad. J. Math.15 (1963) 178-187.  Zbl0108.14304
  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. R.C. Lyndon and M.-P. Shützenberger, The Equation aM = bNcP in a Free Group. Michigan Math. J.9 (1962) 289-298.  
  10. Al.A. Markov, An Example of an Independent System of Words Which Cannot Be Included in a Finite Complete System. Mat. Zametki1 (1967) 87-90.  Zbl0154.00703
  11. A. Restivo, On Codes Having No Finite Completions. Discret Math.17 (1977) 306-316.  Zbl0357.94011
  12. H.J. Shyr, Free Monoids and Languages. Lecture Notes, Hon Min Book Company, Taichung, 2001.  Zbl0746.20050
  13. J.D. Watson and F.C.H. Crick, A Structure for Deoxyribose Nucleic Acid. Nature171 (1953) 737.  

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