Molecular solutions for the set-partition problem on DNA-based computing

Suppose that a finite set S has q elements, and each element in S is a positive integer. The set-partition problem is to determine whether there is a subset TsubeS such that Sigma_xisinT x=Sigma_xisinTmacr x, where Tmacr={x|xisinS and xnotinT}. This paper shows that biological 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 verify our designed molecular solutions for solving the set-partition problem.