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Table 2 Two evaluation algebras for the Sankoff problem

From: Pareto optimization in algebraic dynamic programming

SIGNATURE PROB SIM  
nil \(=\) 0 0  
NoStr (xy) \(=\) x + y x + y  
Split (xy) \(=\) x + y x + y  
Pair \((\langle a, b\rangle , x, \langle c, d\rangle )\) \(=\) x + \(\Psi (a, c)\) + \(\Psi (b, d)\) x + \(\sigma (a,b)\) + \(\sigma (c,d)\) (*)
Ins \((\langle \epsilon , b\rangle )\) \(=\) 0 \(\gamma (b)\)  
Del \((\langle a, \epsilon \rangle )\) \(=\) 0 \(\gamma (a)\)  
Match \((\langle a, b \rangle )\) \(=\) 0 \(\sigma (a,b)\)  
\(\varphi\) \(=\) Max Mx