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An Optical Wavelength-Based Solution to the 3-SAT Problem
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In this paper, an optical wavelength-based method to solve a well-known NP-complete problem 3-SAT is provided. In the 3-SAT problem, a formula F in the form of conjunction of some clauses over Boolean variables is given and the question is to find if F is satisfiable or not. The provided method uses exponential number of different wavelengths in a light ray and considers each group of wavelengths as a possible value-assignment for the variables. It then uses optical devices to drop wavelengths not satisfying F from the light ray. At the end, remaining wavelengths indicate satisfiability of the formula.The method provides two ways to arrange the optical devices to select satisfying wavelengths for a given clause: simple clause selectors and combined clause selectors, both requiring exponential preprocessing time. After preprocessing phase, the provided method requires polynomial time and optical devices to solve each problem instance.