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Upper Bounds on the Computational Power of an Optical Model of Computation

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Algorithms and Computation (ISAAC 2005)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 3827))

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Abstract

We present upper bounds on the computational power of an optical model of computation called the \(\mathcal{C}_{2}\)-CSM. We show that \(\mathcal{C}_{2}\)-CSM time is no more powerful than sequential space, thus giving one of the two inclusions that are necessary to show that the model verifies the parallel computation thesis. Furthermore we show that \(\mathcal{C}_{2}\)-CSMs that simultaneously use polynomial space and polylogarithmic time decide no more than the class NC.

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References

  1. Balcázar, J.L., Díaz, J., Gabarró, J.: Structural complexity. EATCS Monographs on Theoretical Computer Science, vol. I, II. Springer, Berlin (1988)

    MATH  Google Scholar 

  2. Boppana, R.B., Sipser, M.: The complexity of finite functions. In: van Leeuwen (ed.) [19], vol. A (1990)

    Google Scholar 

  3. Borodin, A.: On relating time and space to size and depth. SIAM Journal on Computing 6(4), 733–744 (1977)

    Article  MathSciNet  MATH  Google Scholar 

  4. Chandra, A.K., Stockmeyer, L.J.: Alternation. In: FOCS 1976, Houston, Texas, October 1976, pp. 98–108. IEEE, Los Alamitos (1976)

    Google Scholar 

  5. Furst, M.L., Saxe, J.B., Sipser, M.: Parity, circuits and the polynomial-time hierarchy. Mathematical Systems Theory 17(1), 13–27 (1984)

    Article  MathSciNet  MATH  Google Scholar 

  6. Goldschlager, L.M.: Synchronous parallel computation. PhD thesis, University of Toronto, Computer Science Department (December 1977)

    Google Scholar 

  7. Greenlaw, R., Hoover, H.J., Ruzzo, W.L.: Limits to parallel computation: P-completeness theory. Oxford university Press, Oxford (1995)

    MATH  Google Scholar 

  8. Karp, R.M., Ramachandran, V.: Parallel algorithms for shared memory machines. In: van Leeuwen (ed.) [19], vol. A (1990)

    Google Scholar 

  9. Krapchenko, V.: Asymptotic estimation of addition time of a parallel adder. Syst. Theory Res. 19, 105–222 (1970)

    Google Scholar 

  10. Ladner, R.E., Fischer, M.J.: Parallel prefix computation. Journal of the ACM 27(4), 831–838 (1980)

    Article  MathSciNet  MATH  Google Scholar 

  11. Naughton, T.J.: Continuous-space model of computation is Turing universal. In: Critical Technologies for the Future of Computing, Proc. SPIE, August 2000, vol. 4109, pp. 121–128 (2000)

    Google Scholar 

  12. Naughton, T.J.: A model of computation for Fourier optical processors. In: Optics in Computing 2000, Proc. SPIE, Quebec, June 2000, vol. 4089, pp. 24–34 (2000)

    Google Scholar 

  13. Naughton, T.J., Woods, D.: On the computational power of a continuous-space optical model of computation. In: Margenstern, M., Rogozhin, Y. (eds.) MCU 2001. LNCS, vol. 2055, pp. 288–299. Springer, Heidelberg (2001)

    Chapter  Google Scholar 

  14. Parberry, I.: Parallel complexity theory. Wiley, Chichester (1987)

    MATH  Google Scholar 

  15. Savage, J.E.: Models of computation: Exploring the power of computing. Addison Wesley, Reading (1998)

    MATH  Google Scholar 

  16. Schönhage, A., Strassen, V.: Schnelle multiplikation grosser zahlen. Computing 7(3-4), 281–292 (1971)

    Article  MATH  Google Scholar 

  17. Simon, J.: On feasible numbers. In: Proc. 9th Annual ACM Symposium on Theory of Computing, pp. 195–207. ACM, New York (1977)

    Chapter  Google Scholar 

  18. van Emde Boas, P.: Machine models and simulations. In: van Leeuwen (ed.) [19], vol. A (1990)

    Google Scholar 

  19. van Leeuwen, J. (ed.): Handbook of Theoretical Computer Science, vol. A. Elsevier, Amsterdam (1990)

    Google Scholar 

  20. Woods, D.: Computational complexity of an optical model of computation. PhD thesis, National University of Ireland, Maynooth (2005)

    Google Scholar 

  21. Woods, D., Gibson, J.P.: Complexity of continuous space machine operations. In: Cooper, S.B., Löwe, B., Torenvliet, L. (eds.) CiE 2005. LNCS, vol. 3526, pp. 540–551. Springer, Heidelberg (2005)

    Chapter  Google Scholar 

  22. Woods, D., Gibson, J.P.: Lower bounds on the computational power of an optical model of computation. In: Calude, C.S., Dinneen, M.J., Păun, G., Jesús Pérez-Jímenez, M., Rozenberg, G. (eds.) UC 2005. LNCS, vol. 3699, pp. 237–250. Springer, Heidelberg (2005)

    Chapter  Google Scholar 

  23. Woods, D., Naughton, T.J.: An optical model of computation. Theoretical Computer Science 334(1–3), 227–258 (2005)

    Article  MathSciNet  MATH  Google Scholar 

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Author information

Authors and Affiliations

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

    Damien Woods

Authors
  1. Damien Woods
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Editor information

Editors and Affiliations

  1. Department of Computer Science, City University of Hong Kong, Tat Chee Avenue, Kowloon , Hong Kong

    Xiaotie Deng

  2. Department of Computer Science, University of Texas at Dallas, EE/CS Building, 75083, Richardson, TX, USA

    Ding-Zhu Du

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© 2005 Springer-Verlag Berlin Heidelberg

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Woods, D. (2005). Upper Bounds on the Computational Power of an Optical Model of Computation. In: Deng, X., Du, DZ. (eds) Algorithms and Computation. ISAAC 2005. Lecture Notes in Computer Science, vol 3827. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11602613_78

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  • DOI: https://doi.org/10.1007/11602613_78

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-30935-2

  • Online ISBN: 978-3-540-32426-3

  • eBook Packages: Computer ScienceComputer Science (R0)

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