Finite Completion of comma-free codes Part 1

Nguyen Huong Lam

RAIRO - Theoretical Informatics and Applications (2010)

  • Volume: 38, Issue: 2, page 91-115
  • ISSN: 0988-3754

Abstract

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This paper is the first step in the solution of the problem of finite completion of comma-free codes. We show that every finite comma-free code is included in a finite comma-free code of particular kind, which we called, for lack of a better term, canonical comma-free code. Certainly, finite maximal comma-free codes are always canonical. The final step of the solution which consists in proving further that every canonical comma-free code is completed to a finite maximal comma-free code, is intended to be published in a forthcoming paper.

How to cite

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Lam, Nguyen Huong. "Finite Completion of comma-free codes Part 1." RAIRO - Theoretical Informatics and Applications 38.2 (2010): 91-115. <http://eudml.org/doc/92738>.

@article{Lam2010,
abstract = { This paper is the first step in the solution of the problem of finite completion of comma-free codes. We show that every finite comma-free code is included in a finite comma-free code of particular kind, which we called, for lack of a better term, canonical comma-free code. Certainly, finite maximal comma-free codes are always canonical. The final step of the solution which consists in proving further that every canonical comma-free code is completed to a finite maximal comma-free code, is intended to be published in a forthcoming paper. },
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 = {91-115},
publisher = {EDP Sciences},
title = {Finite Completion of comma-free codes Part 1},
url = {http://eudml.org/doc/92738},
volume = {38},
year = {2010},
}

TY - JOUR
AU - Lam, Nguyen Huong
TI - Finite Completion of comma-free codes Part 1
JO - RAIRO - Theoretical Informatics and Applications
DA - 2010/3//
PB - EDP Sciences
VL - 38
IS - 2
SP - 91
EP - 115
AB - This paper is the first step in the solution of the problem of finite completion of comma-free codes. We show that every finite comma-free code is included in a finite comma-free code of particular kind, which we called, for lack of a better term, canonical comma-free code. Certainly, finite maximal comma-free codes are always canonical. The final step of the solution which consists in proving further that every canonical comma-free code is completed to a finite maximal comma-free code, is intended to be published in a forthcoming paper.
LA - eng
KW - Comma-free code; completion; finite maximal comma-free code.
UR - http://eudml.org/doc/92738
ER -

References

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  1. J. Berstel and D. Perrin, Theory of Codes. Academic Press, Orlando (1985).  Zbl0587.68066
  2. F.H.C. Crick, J.S. Griffith and L.E. Orgel, Codes without Commas. Proc. Natl. Acad. Sci. USA43 (1957) 416-421.  
  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. Selsk23 (1958) 3-34.  
  5. W.L. Eastman, On the Construction of Comma-free Codes. IEEE Trans. Inform. TheoryIT-11 (1965) 263-267.  Zbl0138.15102
  6. C.M. Fan and H.J. Shyr, Some Properties of Maximal Comma-free Codes. Tamkang J. Math.29 (1998) 121-135.  Zbl0978.68088
  7. 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
  8. B.H. Jiggs, Recent Results in Comma-free Codes. Canad. J. Math.15 (1963) 178-187.  Zbl0108.14304
  9. N.H. Lam, Finite Completion of Comma-free Codes. Part I, in Proc. DLT. Springer-Verlag, Lect. Notes Comput. Sci.2450 (2002) 357-368.  
  10. Al. A. Markov, An Example of an Idependent 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. R.A. Scholtz, Maximal and Variable Word-length Comma-free Codes. IEEE Trans. Inform. TheoryIT-15 (1969) 555-559.  Zbl0172.43104
  13. H.J. Shyr, Free Monoids and Languages. Lecture Notes, Hon Min Book Company, Taichung (1991).  Zbl0746.20050
  14. J.D. Watson and F.C.H. Crick, A Structure for Deoxyribose Nucleic Acid. Nature171 (1953) 737.  

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