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.
@article{ITA_2004__38_2_91_0, author = {Lam, Nguyen Huong}, title = {Finite completion of comma-free codes. Part 1}, journal = {RAIRO - Theoretical Informatics and Applications - Informatique Th\'eorique et Applications}, volume = {38}, year = {2004}, pages = {91-115}, doi = {10.1051/ita:2004006}, mrnumber = {2060772}, zbl = {1058.94009}, language = {en}, url = {http://dml.mathdoc.fr/item/ITA_2004__38_2_91_0} }
Lam, Nguyen Huong. Finite completion of comma-free codes. Part 1. RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications, Tome 38 (2004) pp. 91-115. doi : 10.1051/ita:2004006. http://gdmltest.u-ga.fr/item/ITA_2004__38_2_91_0/
[1] Theory of Codes. Academic Press, Orlando (1985). | MR 797069 | Zbl 0587.68066
and ,[2] Codes without Commas. Proc. Natl. Acad. Sci. USA 43 (1957) 416-421. | MR 86734
, and ,[3] Comma-free Codes. Canad. J. Math. 10 (1958) 202-209. | MR 95091 | Zbl 0081.14601
, and ,[4] Construction and Properties of Comma-free Codes. Biol. Medd. Dan. Vid. Selsk 23 (1958) 3-34.
, and ,[5] On the Construction of Comma-free Codes. IEEE Trans. Inform. Theory IT-11 (1965) 263-267. | MR 188006 | Zbl 0138.15102
,[6] Some Properties of Maximal Comma-free Codes. Tamkang J. Math. 29 (1998) 121-135. | MR 1644395 | Zbl 0978.68088
and ,[7] Outfix and Infix Codes and Related Classes of Languages. J. Comput. Syst. Sci. 43 (1991) 484-508. | MR 1135474 | Zbl 0794.68087
, , and ,[8] Recent Results in Comma-free Codes. Canad. J. Math. 15 (1963) 178-187. | MR 143672 | Zbl 0108.14304
,[9] Finite Completion of Comma-free Codes. Part I, in Proc. DLT. Springer-Verlag, Lect. Notes Comput. Sci. 2450 (2002) 357-368. | Zbl 1022.94005
,[10] Al. A. Markov, An Example of an Idependent System of Words Which Cannot Be Included in a Finite Complete System. Mat. Zametki 1 (1967) 87-90. | MR 210594 | Zbl 0154.00703
[11] On Codes Having No Finite Completions. Discret Math. 17 (1977) 306-316. | MR 498922 | Zbl 0357.94011
,[12] Maximal and Variable Word-length Comma-free Codes. IEEE Trans. Inform. Theory IT-15 (1969) 555-559. | MR 250754 | Zbl 0172.43104
,[13] Free Monoids and Languages. Lecture Notes, Hon Min Book Company, Taichung (1991). | MR 1090325 | Zbl 0746.20050
,[14] A Structure for Deoxyribose Nucleic Acid. Nature 171 (1953) 737.
and ,