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Optical Computing and Computational Complexity

  • Conference paper
Unconventional Computation (UC 2006)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 4135))

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Abstract

This work concerns the computational complexity of a model of computation that is inspired by optical computers. The model is called the continuous space machine and operates in discrete timesteps over a number of two-dimensional images of fixed size and arbitrary spatial resolution. The (constant time) operations on images include Fourier transformation, multiplication, addition, thresholding, copying and scaling. We survey some of the work to date on the continuous space machine. This includes a characterisation of the power of an important discrete restriction of the model. Parallel time corresponds, within a polynomial, to sequential space on Turing machines, thus satisfying the parallel computation thesis. A characterisation of the complexity class NC in terms of the model is also given. Thus the model has computational power that is (polynomially) equivalent to that of many well-known parallel models. Such characterisations give a method to translate parallel algorithms to optical algorithms and facilitate the application of the complexity theory toolbox to optical computers. In the present work we improve on these results. Specifically we tighten a lower bound and present some new resource trade-offs.

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Author information

Authors and Affiliations

  1. Boole Centre for Research in Informatics, School of Mathematics, University College Cork, Ireland

    Damien Woods

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  1. Damien Woods
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Editor information

Editors and Affiliations

  1. Department of Computer Science, University of Auckland, New Zealand

    Cristian S. Calude

  2. Department of Computer Science, University of Auckland, 92019, Auckland, New Zealand

    Michael J. Dinneen

  3. Institute of Mathematics of the Romanian Academy, PO Box 1-764, 014700, Bucureşti, Romania

    Gheorghe Păun

  4. Leiden Center of Advanced Computer Science (LIACS), Leiden University, Niels Bohrweg 1, 2333, Leiden, CA, The Netherlands

    Grzegorz Rozenberg

  5. Dept. of Computer Science, University of York,  

    Susan Stepney

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Woods, D. (2006). Optical Computing and Computational Complexity. In: Calude, C.S., Dinneen, M.J., Păun, G., Rozenberg, G., Stepney, S. (eds) Unconventional Computation. UC 2006. Lecture Notes in Computer Science, vol 4135. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11839132_4

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  • DOI: https://doi.org/10.1007/11839132_4

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-38593-6

  • Online ISBN: 978-3-540-38594-3

  • eBook Packages: Computer ScienceComputer Science (R0)

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