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Given a set of strings A jAj = m of strings of length n over an alphabet f0, 1, $g let aij be the j th character of the ith string in A Is there a hitting string x E f0, 1g with jxj = n such that for each ai E A there is some j 0 ::: j < n for which aij and xj (the j th symbol of x) are identical? Without loss of generality we assume that the strings in A are unique since multiple copies of the same string do not affect the selection of x We also throw out all columns that consist entirely of $ character this can be done in O(mn) time If a row consists entirely of $ characters then no solution is possible These pre-processing steps can be performed in O(mn) time A hitting string is sparse if 3j, 0 ::: j < n such that Vi, 0 ::: i < m aij = xj a dense hitting string does not have this property A sparse hitting string can be converted to a dense hitting string in O(mn) using the algorithm described in appendix A