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Words strongly avoiding fractional powers
 Europ. J. of Combinatorics
, 1999
"... Abstract Let k be fixed, 1! k! 2. There exists an infinite word over a finite alphabet which contains no subword of the form xyz with jxyzj=jxyj * k and where z is a permutation of x. 1 Introduction Nonrepetitive words have been studied since Thue [34]. A word is nonrepetitive if it cannot be writt ..."
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Abstract Let k be fixed, 1! k! 2. There exists an infinite word over a finite alphabet which contains no subword of the form xyz with jxyzj=jxyj * k and where z is a permutation of x. 1 Introduction Nonrepetitive words have been studied since Thue [34]. A word is nonrepetitive if it cannot be written xyyz, where x; y; z are words, and y is nonempty. Infinite
Subwords and Power Free Words Are Not Expressible By Word Equations
"... We consider several open problems of Karhumaki, Mignosi, and Plandowski, cf. [KMP], concerning the expressibility of languages and relations as solutions of word equations. We show first that the (scattered) subword relation is not expressible. Then, we consider the set of kpower free finite words ..."
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We consider several open problems of Karhumaki, Mignosi, and Plandowski, cf. [KMP], concerning the expressibility of languages and relations as solutions of word equations. We show first that the (scattered) subword relation is not expressible. Then, we consider the set of kpower free finite words and solve it negativelly for all nontrivial integer values of k. Finally, we consider the Fibonacci finite words. We do not solve the problem of the expressibility of the set of these words but prove that it cannot be given a negative answer (as believed) using the tools in [KMP]. 1
Repetitiveness Of Languages Generated By Morphisms
, 1997
"... We study the repetition of subwords in languages generated by morphisms. First we give a simple proof for the fact that such a language is repetitive if and only if it is strongly repetitive (Ehrenfeucht and Rozenberg, 1983). From this proof we obtain a structurally simple polynomialtime algorithm ..."
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We study the repetition of subwords in languages generated by morphisms. First we give a simple proof for the fact that such a language is repetitive if and only if it is strongly repetitive (Ehrenfeucht and Rozenberg, 1983). From this proof we obtain a structurally simple polynomialtime algorithm for deciding whether such a language is repetitive. Then we give a complete characterization for all those morphisms on a twoletter alphabet that are repetitive. Finally, we characterize those morphisms f on a twoletter alphabet, for which the languages L(f) or SL(f) are regular, respectively contextfree. Acknowledgement: The results presented here were obtained while the second author was visiting at Toho University. He gratefully acknowledges the hospitality of the Faculty of Science of Toho University and the support by the Deutsche Forschungsgemeinschaft. 1 Introduction An important part of formal language theory is concerned with the combinatorial structure of languages. One of ...