An Optical Polynomial Time Solution for the Satisfiability Problem

In this paper, we have used optics to solve the satisfiability problem. The satisfiability problem is a well-known NP-complete problem in computer science, having many real world applications, which no polynomial resources solution is found for it, yet. The provided method in this paper, is based on forming patterns on photographic films iteratively to solve a given satisfiability problem in efficient time. The provided method requires polynomial time, but, exponential length films and exponential amount of energy to solve the satisfiability problem.

[1]  Shlomi Dolev,et al.  Masking traveling beams: Optical solutions for NP-complete problems, trading space for time , 2010, Theor. Comput. Sci..

[2]  Stephen A. Cook,et al.  The complexity of theorem-proving procedures , 1971, STOC.

[3]  Aarti Gupta,et al.  SAT-Based Scalable Formal Verification Solutions , 2007, Series on Integrated Circuits and Systems.

[4]  Saeed Jalili,et al.  An optical solution to the 3-SAT problem using wavelength based selectors , 2010, The Journal of Supercomputing.

[5]  Saeed Jalili,et al.  An Optical Wavelength-Based Solution to the 3-SAT Problem , 2009, OSC.

[6]  Mihai Oltean,et al.  An Optical Solution for the SAT Problem , 2010, OSC.

[7]  Clifford R. Johnson.  Automating the DNA computer: solving n-Variable 3-SAT problems , 2006, Natural Computing.

[8]  Tom Head.  Parallel Computing by Xeroxing on Transparencies , 2009, Algorithmic Bioprocesses.

[9]  Long Gui-Lu,et al.  A Parallel Quantum Algorithm for the Satisfiability Problem , 2008 .

[10]  Ronald L. Rivest,et al.  Introduction to Algorithms , 1990 .

[11]  Saeed Jalili,et al.  Optical Graph 3-Colorability , 2010, OSC.

[12]  Pavel Pudlák,et al.  On the complexity of circuit satisfiability , 2010, STOC '10.

[13]  Arto Salomaa,et al.  Algorithmic Bioprocesses , 2009, Natural Computing Series.

[14]  Saeed Jalili,et al.  Light-based solution for the dominating set problem. , 2012, Applied optics.

[15]  Christel Baier,et al.  Principles of model checking , 2008 .

[16]  José M. García,et al.  Simulating a P system based efficient solution to SAT by using GPUs , 2010, J. Log. Algebraic Methods Program..