International Journal of Foundations of Computer Science ( IF 0.523 ) Pub Date : 2020-08-26 , DOI: 10.1142/s0129054120500288
Hayam Alamro; Mai Alzamel; Costas S. Iliopoulos; Solon P. Pissis; Wing-Kin Sung; Steven Watts

A closed string contains a proper factor occurring as both a prefix and a suffix but not elsewhere in the string. Closed strings were introduced by Fici (WORDS 2011) as objects of combinatorial interest. This paper addresses a new problem by extending the closed string problem to the $k$-closed string problem, for which a level of approximation is permitted up to a number of Hamming distance errors, set by the parameter $k$.

We address the problem of deciding whether or not a given string of length $n$ over an integer alphabet is $k$-closed and additionally specifying the border resulting in the string being $k$-closed. Specifically, we present an $𝒪(kn)$-time and $𝒪(n)$-space algorithm to achieve this along with the pseudocode of an implementation and proof-of-concept experimental results.

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