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On the Computational Power of a Continuous-space Optical Model of Computation

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Machines, Computations, and Universality (MCU 2001)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 2055))

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Abstract

We introduce a continuous-space model of computation. This original model is inspired by the theory of Fourier optics.We show a lower bound on the computational power of this model by Type-2 machine simulation. The limit on computational power of our model is nontrivial. We define a problem solvable with our model that is not Type-2 computable. The theory of optics does not preclude a physical implementation of our model.

Acknowledgements

We gratefully acknowledge advice and assistance from J. Paul Gibson and the Theoretical Aspects of Software Systems research group,NUI Maynooth. Many thanks also to the reviewers of this paper for their constructive comments.

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Authors and Affiliations

  1. TASS Group, Department of Computer Science, National University of Ireland, Maynooth, Ireland

    Thomas J. Naughton & Damien Woods

Authors
  1. Thomas J. Naughton
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  2. Damien Woods
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Editors and Affiliations

  1. LITA, UFR MIM, Université de Metz, Ile du Saulcy, 57045, Metz, Cedex, France

    Maurice Margenstern

  2. Institute of Mathematics and Computer Science of the Academy of Sciences of Moldova, 5 Academiei str, 2028, Chiŗinău, Moldova

    Yurii Rogozhin

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© 2001 Springer-Verlag Berlin Heidelberg

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Naughton, T.J., Woods, D. (2001). On the Computational Power of a Continuous-space Optical Model of Computation. In: Margenstern, M., Rogozhin, Y. (eds) Machines, Computations, and Universality. MCU 2001. Lecture Notes in Computer Science, vol 2055. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-45132-3_20

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  • DOI: https://doi.org/10.1007/3-540-45132-3_20

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-42121-4

  • Online ISBN: 978-3-540-45132-7

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