Solutions of some Classical Problems in Various Theoretical DNA Computing Models

In this work we give efficient molecular computing solutions to eight well-known NP-complete problems, namely the Hamiltonian circuit, Longest path, Longest circuit, Path with forbidden pairs, Monochromatic triangle, Partition into triangles, Partition into paths of length two and Circuit satisfiability problems in the Parallel filtering model of Amos et al. We also show that this model can be simulated in three other models: in the Unrestricted model of Adleman, in the Surface-based model and in the Computing by blocking model, hence the given algorithms can be reformulated in these models as well.