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Zbl 0689.68102
Ratoandromanana, Bodonirina
Codes et motifs. (Codes and motifs). (French)
[J] RAIRO, Inf. Théor. Appl. 23, No.4, 425-444 (1989). ISSN 0988-3754

We prove, for two codes X and Y, the equivalence of the equality $XY=YX$ and the existence of two positive integers i and j such that $X\sp i=Y\sp j$. Moreover, if one of them is singular, these two conditions are equivalent to the existence of a code Z such that X and Y are powers of Z. Then, we show for each non empty language L commuting with a prefix or circular code X, the existence of a code Y, an integer j and $I\subset {\bbfN}$ such that $L=\cup\sb{i\in I}Y\sp i$ and $X=Y\sp j.$ \par In particular, if X is a circular code then $j=1$ and if L is a code, L is a power of X.

MSC 2000:: *68Q45 Formal languages

Keywords: prefix codes

Cited in: Zbl 1079.68051

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