Maňuch, Ján - Defect Effect of Bi-infinite Words in the Two-element Case

dmtcs:279 - Discrete Mathematics & Theoretical Computer Science, January 1, 2001, Vol. 4 no. 2
Defect Effect of Bi-infinite Words in the Two-element Case

Authors: Maňuch, Ján

Let X be a two-element set of words over a finite alphabet. If a bi-infinite word possesses two X-factorizations which are not shiftequivalent, then the primitive roots of the words in X are conjugates. Note, that this is a strict sharpening of a defect theorem for bi-infinite words stated in \emphKMP. Moreover, we prove that there is at most one bi-infinite word possessing two different X-factorizations and give a necessary and sufficient conditions on X for the existence of such a word. Finally, we prove that the family of sets X for which such a word exists is parameterizable.


Volume: Vol. 4 no. 2
Published on: January 1, 2001
Submitted on: March 26, 2015
Keywords: defect effect,bi-infinite words,[INFO.INFO-DM] Computer Science [cs]/Discrete Mathematics [cs.DM]


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