The Overlap Gap Between Left-Infinite and Right-Infinite Words
نویسندگان
چکیده
We study ultimate periodicity properties related to overlaps between the suffixes of a left-infinite word [Formula: see text] and prefixes right-infinite text]. The main theorem states that set minimum lengths words such or is finite, where runs over positive integers are respectively suffix prefix length text], if only ultimately periodic form for some finite
منابع مشابه
Extremal Infinite Overlap-Free Binary Words
Let t be the infinite fixed point, starting with 1, of the morphism μ : 0 → 01, 1→ 10. An infinite word over {0, 1} is said to be overlap-free if it contains no factor of the form axaxa, where a ∈ {0, 1} and x ∈ {0, 1}∗. We prove that the lexicographically least infinite overlap-free binary word beginning with any specified prefix, if it exists, has a suffix which is a suffix of t. In particula...
متن کاملLength-k-overlap-free Binary Infinite Words
We study length-k-overlap-free binary infinite words, i.e., binary infinite words which can contain only overlaps xyxyx with |x| ≤ k− 1. We prove that no such word can be generated by a morphism, except if k = 1. On the other hand, for every k ≥ 2, there exist length-k-overlap-free binary infinite words which are not length-(k−1)-overlap-free. As an application, we prove that, for every non-neg...
متن کاملOverlap-freeness in infinite partial words
10 We prove that there exist infinitely many infinite overlap-free binary partial words. 11 Moreover, we show that these words can contain only one hole and the hole must 12 occur either in the first or in the second position. We define that a partial word is 13 k-overlap-free if it does not contain a factor of the form xyxyx where the length 14 of x is at least k. We prove that there exist inf...
متن کاملInfinite permutations vs. infinite words
I am going to compare well-known properties of infinite words with those of infinite permutations, a new object studied since middle 2000s. Basically, it was Sergey Avgustinovich who invented this notion, although in an early study by Davis et al. [4] permutations appear in a very similar framework as early as in 1977. I am going to tell about periodicity of permutations, their complexity accor...
متن کاملOn the Frequency and Periodicity of Infinite Words On the Frequency and Periodicity of Infinite Words
This work contributes to two aspects of the understanding of infinite words: the frequency of letters in a morphic sequence and periodicity considerations on infinite words. First, we develop a necessary and sufficient criteria for the existence of the frequency of a letter in a morphic sequence, and give some applications of this result. We show that the frequencies of all letters exist in pur...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: International Journal of Foundations of Computer Science
سال: 2021
ISSN: ['1793-6373', '0129-0541']
DOI: https://doi.org/10.1142/s0129054121500350