Inferring strings from Lyndon factorization

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抄録

The Lyndon factorization of a string w is a unique factorization ℓ1 p1 ,…,ℓm pm of w such that ℓ1,…,ℓm is a sequence of Lyndon words that is monotonically decreasing in lexicographic order. In this paper, we consider the reverse-engineering problem on Lyndon factorization: Given a sequence S=((s1,p1),…,(sm,pm)) of ordered pairs of positive integers, find a string w whose Lyndon factorization corresponds to the input sequence S, i.e., the Lyndon factorization of w is in a form of ℓ1 p1 ,…,ℓm pm with |ℓi|=si for all 1≤i≤m. Firstly, we show that there exists a simple O(n)-time algorithm if the size of the alphabet is unbounded, where n is the length of the output string. Secondly, we present an O(n)-time algorithm to compute a string over an alphabet of the smallest size. Thirdly, we show how to compute only the size of the smallest alphabet in O(m) time. Fourthly, we give an O(m)-time algorithm to compute an O(m)-size representation of a string over an alphabet of the smallest size. Finally, we propose an efficient algorithm to enumerate all strings whose Lyndon factorizations correspond to S.

元の言語 英語 147-156 10 Theoretical Computer Science 689 https://doi.org/10.1016/j.tcs.2017.05.038 出版済み - 8 15 2017

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Factorization
Strings
p.m.
Lyndon Words
Unique factorisation
Lexicographic Order
Ordered pair
Reverse engineering
Reverse Engineering
Efficient Algorithms
Integer
Output

All Science Journal Classification (ASJC) codes

• Theoretical Computer Science
• Computer Science(all)

これを引用

Inferring strings from Lyndon factorization. / Nakashima, Yuto; Okabe, Takashi; I, Tomohiro; Inenaga, Shunsuke; Bannai, Hideo; Takeda, Masayuki.

：: Theoretical Computer Science, 巻 689, 15.08.2017, p. 147-156.

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