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Computation with optical sensitive sheets

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Abstract

In this paper, we provide a new optical model for computation, which is named filter machine. Filter machine consists of optical filters as data storage and imaging operation for computation. Each filter is a long optical sensitive sheet, divided into cells. Filter cells may represent different patterns of opaque and transparent cells which are constructed by emitting light to some cells and made them opaque. The computation in filter machines starts from basic filters with basic patterns of opaque and transparent cells. We provide an algorithm that, given a Boolean circuit, produces a filter machine generating output of the circuit for all possible inputs. Thus, we show that the filter machine is able to generate every Boolean function. Indeed, the number of required cells in each filter is exponential according to the number of variables in the given Boolean function. In order to show the efficiency of the model in solving combinatorial problems, we provide a solution for the k-clique problem on graphs by filter machines, which requires polynomial time and number of filters but exponential number of cells in each filter.

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References

  • Barakat R, Reif JH (1987) Polynomial convolution algorithm for matrix multiplication with application for optical computing. J Appl Optics 26(14):2707–2711

    Article  Google Scholar 

  • Cormen TH, Leiserson CE, Rivest RL, Stein C (2001) Introduction to algorithms, vol 2. The MIT Press, Cambridge

    MATH  Google Scholar 

  • Dolev S, Fitoussi H (2007) The traveling beams optical solutions for bounded NP-complete problems. In: Fun With Algorithms. Volume 4475 of Lecture Notes in Computer Science., Springer-Verlag, Heidelberg, pp 120–134

  • Dolev S, Fitoussi H (2010) Masking traveling beams: optical solutions for np-complete problems, trading space for time. Theor Comput Sci 411:837–853

    Article  MathSciNet  MATH  Google Scholar 

  • Eyal C, Shlomi Dolev SF, Puzis R, Rosenblit M (2011) Nanotechnology based optical solution for np-hard problems. In: OSC 2010. Volume 6748 of Lecture Notes in Computer Science., Springer-Verlag, Heidelberg, pp 86–99

  • Goliaei S, Foroughmand-Araabi MH (2013) Light ray concentration reduces the complexity of the wavelength-based machine on pspace languages. In: Mauri G, Dennunzio A, Manzoni L, Porreca A (eds) UCNC 2013, vol 7956., Lecture notes in computer scienceSpringer-Verlag, Heidelberg, pp 90–101

    Google Scholar 

  • Goliaei S, Jalili S (2009) An optical wavelength-based solution to the 3-SAT problem. In: Dolev S, Oltean M (eds) OSC 2009, vol 5882., Lecture notes in computer scienceSpringer-Verlag, Berlin Heidelberg, pp 77–85

    Google Scholar 

  • Goliaei S, Jalili S (2011) Optical graph 3-colorability. In: Dolev S, Oltean M (eds) OSC 2010, vol 6748, Lecture notes in computer scienceSpringer-Verlag, Berlin Heidelberg, pp 16–22

    Google Scholar 

  • Goliaei S, Jalili S (2012) An optical solution to the 3-SAT problem using wavelength based selectors. J Supercomput 62:663–672

    Article  Google Scholar 

  • Goliaei S, Jalili S, Salimi J (2012) Light-based solution for the dominating set problem. Appl Optics 51(29):6979–6983

    Article  Google Scholar 

  • Goliaei S, Jalili S (2013a) An optical wavelength-based computational machine. Int J Unconv Comput 9(1–2):97–123

    Google Scholar 

  • Goliaei S, Jalili S (2013b) An optical polynomial time solution for the satisfiability problem. In: Dolev S, Oltean M (eds) OSC 2012, vol 7715, Lecture notes in computer scienceSpringer-Verlag, Heidelberg, pp 15–24

    Google Scholar 

  • Haist T, Osten W (2007) An optical solution for the traveling salesman problem. Optics Express 15(16):10473–10482

    Article  Google Scholar 

  • Levinson HJ (2005) Proximity x-ray lithography, vol 2. SPIE Press, Bellingham

    Google Scholar 

  • Muntean O, Oltean M (2009) Deciding whether a linear diophantine equation has solutions by using a light-based device. J Optoelectron Adv Mater 11(11):1728–1734

    Google Scholar 

  • Oltean M (2008) Solving the hamiltonian path problem with a light-based computer. Nat Comput 6(1):57–70

    Article  MathSciNet  Google Scholar 

  • Oltean M (2009) Light-based string matching. Nat Comput 8(1):121–132

    Article  MathSciNet  MATH  Google Scholar 

  • Oltean M, Muntean O (2011) An optical solution for the sat problem. In: Dolev S, Oltean M (eds) Lecture notes in computer science. Springer-Verlag, Berlin, Heidelberg, pp 53–62

    Google Scholar 

  • Reif JH, Tyagi A (1990) Energy complexity of optical computations. In: Proceedings of the 2nd IEEE Symposium on Parallel and Distributed Processing, pp 14–21

  • Woods D, Naughton TJ (2009) Optical computing. Appl Math Comput 215(4):1417–1430

    Article  MathSciNet  MATH  Google Scholar 

Download references

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Authors and Affiliations

  1. University of Tehran, Tehran, Iran

    Sama Goliaei

  2. Tarbiat Modares University, Tehran, Iran

    Saeed Jalili

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  1. Sama Goliaei
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  2. Saeed Jalili
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Correspondence to Sama Goliaei.

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Goliaei, S., Jalili, S. Computation with optical sensitive sheets. Nat Comput 14, 437–450 (2015). https://doi.org/10.1007/s11047-014-9447-4

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  • DOI: https://doi.org/10.1007/s11047-014-9447-4

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