A similar duality holds for global alignment: there is a direct correspondence between maximizing score and minimizing cost (Smith, Waterman, and Fitch 1981; Eizenga and Paten 2022): given a scoring model with fixed affine costs \(\delta(a, a) = M\), \(\delta(a,b) = X\), and \(w_k = O + E \cdot k\), there is a cost-model (with \(\delta(a,a)=0\)) that yields the same optimal alignment.