Molecular Solutions For The Set-Partition Problem On Dna-Based Computing

Consider that the every element in a finite set S having q elements is a positive integer. The set-partition problem is to determine whether there is a subset T ⊆ S such that , ∑X_X∈T = ∑X_X∈̅T where ̅T = {xl x ∈ S and x ∉ T}. This research demonstrates that molecular operations can be applied to solve the set-partition problem. In order to perform this goal, we offer two DNA-based algorithms, an unsigned parallel adder and a parallel Exclusive-OR (XOR) operation, that formally demonstrate our designed molecular solutions for solving the set-partition problem.