Fast parallel molecular solutions for DNA-based supercomputing: the subset-product problem

In this paper our main purpose is to give molecular solutions for the subset-product problem. In order to achieve this, we propose three DNA-based algorithms - parallel adder, parallel multiplier and parallel comparator - that formally verify our designed molecular solutions for the subset-product problem. We also show that Boolean circuits are not needed to perform mathematical operations on a molecular computer. Furthermore, this work indicates that the subset-product problem is solved and also presents clear evidence of the ability of molecular computing to perform complicated mathematical operations.