Abstract
Classes of codes defined by binary relations are considered. It turns out that many classes of codes can be defined by length-increasing transitive binary relations. By introducing a general embedding schema we show that the embedding problem can be solved in a unified way for many classes of codes defined in such a way. Several among these classes of codes can be characterized by means of variants of Parikh vectors. This is very useful in constructing many-word concrete codes, maximal codes in corresponding classes of codes. Also, this allows to establish procedures to generate all maximall codes as well as algorithms to embed a code in a maximal one in some classes of codes.
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References
Berstel, J., Perrin, D.: Theory of Codes. Academic Press, New York (1985)
Bruyère, V., Latteux, M.: Variable-length maximal codes. Theoretical Computer Science 98, 321–337 (1992)
Bruyère, V., Wang, L., Zhang, L.: On completion of codes with finite deciphering delay. European Journal of Combinatorics 11, 513–521 (1990)
Ehrenfeucht, A., Rozenberg, G.: Each regular code is included in a maximal regular code. RAIRO Theoretical Informatics and Applications 20, 89–96 (1986)
Grätzer, G.: Universal Algebra. Van Nostrand, Princeton (1968)
Hung, K.V., Huy, P.T., Van, D.L.: On some classes of codes defined by binary relations. Acta Mathematica Vietnamica 29, 163–176 (2004)
Hung, K.V., Huy, P.T., Van, D.L.: Codes concerning roots of words. Vietnam Journal of Mathematics 32, 345–359 (2004)
Hopcroft, J., Ullman, J.: Formal Languages and Their Relation to Automata. Addison-Wesley Publishing Company, Massachussetts (1969)
Ito, M., Jürgensen, H., Shyr, H., Thierrin, G.: Outfix and infix codes and related classes of languages. Journal of Computer and System Science 43, 484–508 (1991)
Ito, M., Thierrin, G.: Congruences, infix and cohesive prefix codes. Theoretical Computer Science 136, 471–485 (1994)
Jürgensen, H., Konstatinidis, S.: Codes. In: Rozenberg, G., Salomaa, A. (eds.) Handbook of Formal Languages, pp. 511–607. Springer, Berlin (1997)
Lam, N.H.: Finite maximal infix codes. Semigroup Forum 61, 346–356 (2000)
Markov, A.A.: An example of an independent system of words which cannot be included in a finite complete system. Matematicheskie Zametki 1, 87–90 (1967) (in Russian)
Perrin, D.: Completing biprefix codes. Theoretical Computer Science 28, 329–336 (1984)
Restivo, A.: On codes having no finite completion. Discrete Mathematics 17, 309–316 (1977)
Restivo, A., Salemi, S., Sportelli, T.: Completing codes. RAIRO Theoretical Informatics and Applications 23, 135–147 (1989)
Shyr, H.: Free Monoids and Languages. Hon Min Book Company, Taichung (1991)
Shyr, H., Thierrin, G.: Codes and binary relations. In: Lecture Notes 586 “Sèminarie d’Algèbre, Paul Dubreil, Paris, pp. 180–188. Springer, Heidelberg (1975-1976)
Van Embedding, D.L.: problem for codes defined by binary relations. Preprint 98/A22, Institute of Mathematics, Hanoi (1998)
Van, D.L.: On a class of hypercodes. In: Ito, M., Imaoka, T. (eds.) Words, Languages and Combinatorics III, pp. 171–183. World Scientific, Singapore (2003)
Van, D.L., Hung, K.V.: On codes defined by binary relations, Part I: Embedding problem (submitted)
Van, D.L., Hung, K.V.: On codes defined by binary relations, Part II: Vector characterizations and maximality (submitted)
Zhang, L., Shen, Z.: Completion of recognizable bifix codes. Theoretical Computer Science 145, 345–355 (1995)
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Van, D.L., Van Hung, K., Huy, P.T. (2005). Codes and Length-Increasing Transitive Binary Relations. In: Van Hung, D., Wirsing, M. (eds) Theoretical Aspects of Computing – ICTAC 2005. ICTAC 2005. Lecture Notes in Computer Science, vol 3722. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11560647_2
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DOI: https://doi.org/10.1007/11560647_2
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