The Complexity Of The NP-Class

This paper presents a novel and straight formulation, and gives a complete insight towards the understanding of the complexity of the problems of the so called NP-Class. In particular, this paper focuses in the Searching of the Optimal Geometrical Structures and the Travelling Salesman Problems. The main results are the polynomial reduction procedure and the solution to the Noted Conjecture of the NP-Class

The 2-local Hamiltonian problem encompasses NP

We show that the NP complete problems MAX CUT and INDEPENDENT SET can be formulated as the 2-local Hamiltonian problem as defined by Kitaev. He introduced the quantum complexity class BQNP as the quantum analog of NP, and showed that the 5-local Hamiltonian problem is BQNP-complete. It is not known whether the s-local Hamiltonian problem is BQNP-complete for s smaller than 5. Therefore it is interesting to determine what problems can be reduced to the s-local Hamiltonian problem. Kitaev showed that 3-SAT can be formulated as a 3-local Hamiltonian problem. We extend his result by showing that 2-locality is sufficient in order to encompass NP.Comment: 7 page