Expressing an NP-Complete Problem as the Solvability of a Polynomial Equation

Details Expressing an NP-Complete Problem as the Solvability of a Polynomial Equation Expressing an NP-Complete Problem as the Solvability of a Polynomial Equation

2007-07-09

arxiv.org/abs/0707.1176v2

Computer Science

Computational Complexity

7 pages

Scientific paper

We demonstrate a polynomial approach to express the decision version of the directed Hamiltonian Cycle Problem (HCP), which is NP-Complete, as the Solvability of a Polynomial Equation with a constant number of variables, within a bounded real space. We first introduce four new Theorems for a set of periodic Functions with irrational periods, based on which we then use a trigonometric substitution, to show how the HCP can be expressed as the Solvability of a single polynomial Equation with a constant number of variables. The feasible solution of each of these variables is bounded within two real numbers. We point out what future work is necessary to prove that P=NP.

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