We describe here an optical device, based on time-delays, for solving the set splitting problem which is well-known NP-complete problem. The device has a graph-like structure and the light is traversing it from a start node to a destination node. All possible (potential) paths in the graph are generated and at the destination we will check which one satisfies completely the problem's constrains.

[1] R.S. Braich, N. Chelyapov, C. Johnson, P. Rothemund, L. Adleman, Solution of a 20-variable 3-SAT problem on a DNA computer , Science 296, 5567 (2002) 499-502. ⇒140, 141

[2] S. Dolev, H. Fitoussi, The traveling beams optical solutions for bounded NP- complete problems, Int. Conf. on Fun with Algorithms, FUN 2007, LNCS 4475, pp. 120-134, 2007. ⇒134

[3] M. R. Garey, D. S. Johnson, Computers and intractability: A guide to NP-Completeness, Freeman & Co, San Francisco, CA, 1979. ⇒134, 135

[4] S. Goliaei. S. Jalili, An optical wavelength-based solutionto the 3-SAT problem, Int. Workshop on Optical Supercomputing OSC 2009, LNCS 5882, pp. 77-85, Springer-Verlag Heidelberg, 2009. ⇒134

[5] S. Goliaei. S. Jalili, Optical graph 3-colorability, Int. Workshop on Optical Supercomputing, OSC 2010 LNCS 6748, pp. 16-22, Springer-Verlag Heidelberg, 2011. ⇒134

[6] S. Goliaei, M-H. Foroughman-Araabi, Lower bounds on the complexity of the wavelength-based machine, Int. Conference on Unconventional Computing and Natural Computation, UCNC 2012 LNCS 7445, pp. 94-105, Springer-Verlag Heidelberg, 2012. ⇒134

[7] S. Goliaei, S. Jalili, J. Salimi, Light-based solution for the dominating set prob- lem, Applied Optics 51,, 29 (2012) 6979-6983. ⇒134

[8] S. Goliaei, S. Jalili, An optical solution to the 3-SAT problem using wave-length based selectors, Int. Journal of Supercomputing 62, 2 (2012) 663-672. ⇒134

[9] S. Goliaei, S. Jalili, An optical polynomial time solution for the satisfiability problem, Int. Workshop on Optical Supercomputing, OSC 2012, LNCS 7715, pp. 15-24, Springer-Verlag Heidelberg, 2013. ⇒134

[10] S. Goliaei, M-H. Foroughman-Araabi, Light ray concentration reduces the complexity of the wavelength-based machine on PSPACE languages, Int. Conf. on Unconventional Computing and Natural Computation, UCNC 2013, LNCS 7956, pp. 90-101, Springer-Verlag Heidelberg, 2013. ⇒134

[11] S. Goliaei, M-H. Foroughman-Araabi, On the complexity of nonuniform wavelength-based machine, Natural Computing 13, 2 (2014) 269-283. ⇒134

[12] S. Goliaei, S. Jalili, Computation with optical sensitive sheets, Natural Comput- ing 14, 3 (2015) 437-450. ⇒134

[13] T. Haist, W. Osten, An optical solution for the traveling salesman problem, Opt. Express 15, 16 (2007) 10473-10482. ⇒134

[14] T. Haist, W Osten, An optical solution for the traveling salesman prob- lem:erratum, Opt. Express 15, 20 (2007) 12627-12627. ⇒134

[15] T. Haist, W. Osten, Ultrafast digital-optical arithmetic using wave-optical com- puting, Int. Workshop on Optical Supercomputing, OSC 2008, LNCS 5172, pp. 33-45, 2008. ⇒134

[16] T. Haist, W. Osten, Proposal for secure key distribution using classical optics, Int. Workshop on Optical Supercomputing, OSC 2009, LNCS 5882, pp. 99-101, 2009. ⇒134

[17] R. Hasan, S. Rahman, Computing a solution for the subset sum problem with a light based device, Int. Workshop on Optical Supercomputing, OSC 2009, LNCS 5882, pp. 70-76, 2009. ⇒134

[18] T. Head, Parallel computing by xeroxing on transparencies, Algorithmic Biopro- cesses, pp. 631-637, 2009. ⇒134

[19] T. Head, Computing transparently: the independent sets in a graph, Natural Computing, 10, 1 (2011) 129-138. ⇒134

[20] K. Nitta, N. Katsuta, O. Matoba, Improvement of a system for prime factoriza- tion based on optical interferometer, Int. Workshop on Optical Supercomputing, OSC 2009, LNCS 5882, pp. 124-129, 2009. ⇒134

[21] K. Nitta, N. Katsuta, O. Matoba, A method for modulo operation by use of spatial parallelism, Int. Workshop on Optical Supercomputing, OSC 2008, LNCS 5172, pp. 98-103, 2008. ⇒134

[22] O. Muntean, Optical Solutions for NP-complete problems (graduation thesis), Faculty of Mathematics and Computer Science, Babeş-Bolyai University, Cluj- Napoca, Romania (defended 3rd of July, 2007). )134

[23] O. Muntean, M. Oltean, Using light for solving the unbounded subset-sum prob-lem, Int. J. of Innovative Computing, Information and Control 5, 8 (2009) 2159{2167. )134

[24] O. Muntean, M. Oltean, Deciding whether a linear Diophantine equation has so-lutions by using a light-based device, J. Optoelectronics and Advanced Materials,11, 11 (2009) 1728{1734. )134

[25] M. Oltean, A light-based device for solving the Hamiltonian path problem, Int.Conf. on Unconventional Computation, UC 2006, LNCS 4135, Springer-Verlag,pp. 217{227, 2006. )134, 135, 140

[26] M. Oltean M., O. Muntean, Solving the subset-sum problem with a light-baseddevice, Natural Computing, 8, 2 (2009) 321{331. )134, 135, 136, 137, 139, 141

[27] M. Oltean, O. Muntean, Exact cover with light, New Generation Computingn,26, 4 (2008) 327{344. )134

[28] M. Oltean, O. Muntean, An optical solution for the SAT problem, Int. Workshopon Optical Supercomputing, OSC 2010, LNCS 6748, pp. 53{62, 2010. )134

[29] N. T. Shaked, S. Messika, S. Dolev, J. Rosen, Optical solution for bounded NP-complete problems, Applied Optics 46, 5 (2007) 711{724. )134

[30] N. Shakeri, S. Jalili, V. Ahmadi, A. R. Zali, S. Goliaei, A 2-dimensional op-tical architecture for solving Hamiltonian path problem based on micro ringresonators, Optics & Laser Technology, 65, 1 (2015) 56{65. )134, 140

[31]*** Set splitting problem on Wikipedia, https://en.wikipedia.org/wiki/Set_splitting_problem, last accessed on 2017.10.09 )135