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Abstract: We prove computability and complexity results for an original model of computation. Our model is inspired by the theory of Fourier optics. We prove our model can simulate analog recurrent neural networks, thus establishing a lower bound on its computational power. We also prove some computational complexity results for searching and sorting algorithms expressed with our model. (Update)
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BibTeX entry: (Update)
@misc{ woods-analog,
author = "Damien Woods and Thomas J. Naughton and J. Paul Gibson",
title = "Analog Recurrent Neural Network Simulation, Θ(log_2 n) Unordered
Search, and Bitonic Sort with an Optically-Inspired Model of Computation",
url = "citeseer.ist.psu.edu/article/woods01analog.html" }
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102 Strengths and weaknesses of quantum computing - Bennett, Bernstein et al. - 1997
61 Analog computation via neural networks - Siegelmann, Sontag - 1994
59 Parallel Sorting Algorithms (context) - Akl - 1985
36 Neural networks and analog computation: beyond the Turing li.. (context) - Siegelmann - 1999
28 Vol 3: Sorting and Searching (context) - Knuth, of - 1973
28 Parallel Computation Models and Methods (context) - Akl - 1997
16 A model of computation for Fourier optical processors - Naughton - 2000
14 Conditional branching is not necessary for universal computa.. - Rojas - 1996
13 General-purpose acousto-optic connectionist processor - Naughton, Javadpour et al. - 1999
12 and Joaquim Gabarr o (context) - Balc, Josep et al. - 1988
7 the computational power of a continuous-space optical model .. - Naughton, Woods - 2055
4 Bitonic sorting using an optoelectronic recirculating archit.. (context) - Beyette, Mitkas et al. - 1994
4 Formal engineering of the bitonic sort using PVS - Couturier - 1998
3 An optical sorting algorithm for meshconnected computers (context) - Schnorr, Shamir - 1986
3 Constant-time parallel sorting algorithm and its optical imp.. - Louri, Hatch et al. - 1995
3 sorting network (context) - Ajati, Kmolos et al. - 1983
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