Abstract
This study extends the understanding of two-element pure codes. Some characteristics of different length two-element pure codes are studied. It is shown that a language is a pure code which contains two distinct primitive words u and v with different lengths if and only if the regular expression u + v + of the two distinct words u and v is primitive.
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References
De Luca A.: On the combinatorial problems in free monoids. Discrete Math. 38, 207–225 (1982)
Fan C.-M., Shyr H.J.: δ-codes and δ-languages. J. Discrete Math. Cryptogr. 8(3), 381–394 (2005)
Fan C.-M., Huang C.C.: Properties of pure codes. Int. J. Comput. Math. 85(1), 9–17 (2008)
Lyndon R.C., Schützenberger M.P.: On the equation a M = b N c P in a free group. Michigan Math. J. 9, 289–298 (1962)
Restivo A.: On a question of McNaughton and Papert. Inform. Control 25, 93–101 (1974)
Shyr H.J., Thierrin G.: Codes, languages and \({\rm MO}{{\overline{\rm L}}}\) schemes. RAIRO Inform. Théor./Theoret. Comput. Sci. 1(4), 293–301 (1997)
Shyr, H.J., Thierrin, G.: Disjunctive languages and codes, fundamentals of computation theory. In: Proceedings of the 1977 International FCT-Conference. Lecture Notes in Computer Science, Springer, Poznan Poland, vol. 5, pp. 171–176 (1997)
Shyr H.J., Yu S.S.: Non-primitive words in the language p + q +. Soochow J. Math. 20(4), 535–546 (1994)
Yu S.S.: Palindrome words and reverse closed languages. Int. J. Comput. Math. 75, 389–402 (2000)
Yu S.S.: Factorization in the monoid of languages. Soochow J. Math. 30(1), 103–125 (2004)
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Huang, C.C. A note on pure codes. Acta Informatica 47, 347–357 (2010). https://doi.org/10.1007/s00236-010-0122-7
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DOI: https://doi.org/10.1007/s00236-010-0122-7