Definition 1 (Patter)
A pattern is a contiguous sub-sequence of DNA sequence S drawn from Σ = {A, C, G, T}. A sequence α = 〈a1, a2, ..., an〉 is called a contiguous sub-sequence of another sequence β = 〈b1, b2, ..., bm〉, and β is a contiguous super-sequence of α, denoted as α⊆β, if there exists integers 1 ≤ j1 ≤ j2 ≤ ... ≤ jn ≤ m and ji+1 = ji + 1 for 1 ≤ i ≤ n-1 such that a1 = bj1, a2 = bj2, ..., an = bjn. We can also say that α is contained by β. In our paper, we use the term "(sub)-sequence" to describe "contiguous (sub)-sequence" in brief.