Overlap-freeness in infinite partial words



: Halava V, Harju T, Karki T, Seebold P

Publisher: ELSEVIER SCIENCE BV

: 2009

: Theoretical Computer Science

: THEORETICAL COMPUTER SCIENCE

: THEOR COMPUT SCI

: 410

: 8-10

: 943

: 948

: 6

: 0304-3975

DOI: https://doi.org/10.1016/j.tcs.2008.12.041


We prove that there exist infinitely many infinite overlap-free binary partial words containing at least one hole. Moreover, we show that these words cannot contain more than one hole and the only hole must Occur either in the first or in the second position. We define that a partial word is k-overlap-free if it does not contain a factor of the form xyxyx where the length of x is at least k. We prove that there exist infinitely many 2-overlap-free binary partial words containing an infinite number of holes. (C) 2009 Elsevier B.V. All rights reserved.



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