The index of a binary word

Authors:
Aleksandar Ili;Sandi Klavar;Yoomi Rho
Affiliations:
Faculty of Sciences and Mathematics, University of Ni, Serbia;Faculty of Mathematics and Physics, University of Ljubljana, Slovenia and Faculty of Natural Sciences and Mathematics, University of Maribor, Slovenia;Department of Mathematics, University of Incheon, Republic of Korea
Venue:
Theoretical Computer Science
Year:
2012

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Abstract

A binary word u is f-free if it does not contain f as a factor. A word f is d-good if for any f-free words u and v of length d, v can be obtained from u by complementing one by one the bits of u on which u and v differ, such that all intermediate words are f-free. We say that f is good if it is d-good for any d=1. A word is bad if it is not good. The index @b(f) of f is the smallest integer d such that f is not d-good, so that @b(f)