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Linear time recognition of squarefree strings. (English) Zbl 0572.68068

Combinatorial algorithms on words, Proc. NATO Adv. Res. Workshop, Maratea/Italy 1984, NATO ASI Ser., Ser. F 12, 271-278 (1985).
[For the entire collection see Zbl 0564.00027.]
A square is an immediately repeated nonempty string, e.g., aa, abab, abcabc. This paper presents a new O(n log n) algorithm to determine whether a string of length n has a substring which is a square. The algorithm is not as general as some previous algorithms for finding all squares, but it does have a simplicity which the others lack. Also, for a fixed alphabet of size k, the algorithm can be improved by a factor of \(\log_ k(n)\), yielding an O(n) algorithm for determining whether a string contains a square.

MSC:

68Q45 Formal languages and automata

Citations:

Zbl 0564.00027