Separable Attributes: a Technique for Solving the Summary: Separable Attributes: a Technique for Solving the Sub Matrices Character Count Problem Amihood Amir  Kenneth W. Church y Emanuel Dar z AT&T Labs AT&T Labs Bar-Ilan University and Bar-Ilan University Abstract The subsequence character count problem has as its input an array S = s 1 ; :::; s n of symbols over alphabet  and a natural number m. Its output is: for every i; i = 1; :::; n m + 1; the number of di erent alphabet symbols occurring in the subsequence s i ; s i+1 ; :::; s i+m 1 . The subsequence character count problem is a natural problem that has many uses. It can be solved in linear time for xed nite alphabets and in time O(n log m) for in nite alphabets. The character count problem can be generalized to two dimensions and becomes the sub- matrix character count problem. Its input is an n  n matrix T over alphabet  and a natural number m. Its output is: for every i; j; i; j = 1; :::; n m+ 1; the number of di erent alphabet symbols occurring in the submatrix T [i + k; j + `]; k = 0; :::; m 1; ` = 0; :::; m 1. The straightforward one dimensional solution slides a window along the text adding an element and deleting an element at every step. The problem with two dimensions is that at every move of the window there are m elements added and m deleted. Collections: Mathematics