Before revision:  Finally, we show that if the input strings do not have long highly periodic substrings, then the gap edit distance problem can be solved in sublinear time within any factor \alpha>1.\tilde{O}{\epsilon^2 k}+k^2\ell).
After revision:  Finally, we show that if the input strings do not have long highly periodic substrings, then the gap edit distance problem can be solved in sublinear time . Specifically, if the strings contain no substring of length \ell with period at most 2k, then the running time we achieve is\tilde{O}{\epsilon^2 k}+k^2\ell).