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Special Purpose Parallel Computing
 Lectures on Parallel Computation
, 1993
"... A vast amount of work has been done in recent years on the design, analysis, implementation and verification of special purpose parallel computing systems. This paper presents a survey of various aspects of this work. A long, but by no means complete, bibliography is given. 1. Introduction Turing ..."
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Cited by 77 (5 self)
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A vast amount of work has been done in recent years on the design, analysis, implementation and verification of special purpose parallel computing systems. This paper presents a survey of various aspects of this work. A long, but by no means complete, bibliography is given. 1. Introduction Turing [365] demonstrated that, in principle, a single general purpose sequential machine could be designed which would be capable of efficiently performing any computation which could be performed by a special purpose sequential machine. The importance of this universality result for subsequent practical developments in computing cannot be overstated. It showed that, for a given computational problem, the additional efficiency advantages which could be gained by designing a special purpose sequential machine for that problem would not be great. Around 1944, von Neumann produced a proposal [66, 389] for a general purpose storedprogram sequential computer which captured the fundamental principles of...
A Survey of ContinuousTime Computation Theory
 Advances in Algorithms, Languages, and Complexity
, 1997
"... Motivated partly by the resurgence of neural computation research, and partly by advances in device technology, there has been a recent increase of interest in analog, continuoustime computation. However, while specialcase algorithms and devices are being developed, relatively little work exists o ..."
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Cited by 30 (6 self)
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Motivated partly by the resurgence of neural computation research, and partly by advances in device technology, there has been a recent increase of interest in analog, continuoustime computation. However, while specialcase algorithms and devices are being developed, relatively little work exists on the general theory of continuoustime models of computation. In this paper, we survey the existing models and results in this area, and point to some of the open research questions. 1 Introduction After a long period of oblivion, interest in analog computation is again on the rise. The immediate cause for this new wave of activity is surely the success of the neural networks "revolution", which has provided hardware designers with several new numerically based, computationally interesting models that are structurally sufficiently simple to be implemented directly in silicon. (For designs and actual implementations of neural models in VLSI, see e.g. [30, 45]). However, the more fundamental...
Optical solution for bounded NPcomplete problems
 Appl. Opt
, 2007
"... We present a new optical method for solving bounded (inputlengthrestricted) NPcomplete combinatorial problems. We have chosen to demonstrate the method with an NPcomplete problem called the traveling salesman problem (TSP). The power of optics in this method is realized by using a fast matrix–ve ..."
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Cited by 14 (6 self)
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We present a new optical method for solving bounded (inputlengthrestricted) NPcomplete combinatorial problems. We have chosen to demonstrate the method with an NPcomplete problem called the traveling salesman problem (TSP). The power of optics in this method is realized by using a fast matrix–vector multiplication between a binary matrix, representing all feasible TSP tours, and a grayscale vector, representing the weights among the TSP cities. The multiplication is performed optically by using an optical correlator. To synthesize the initial binary matrix representing all feasible tours, an efficient algorithm is provided. Simulations and experimental results prove the validity of the new
Efficient Parallel Algorithms for Optical Computing with the DFT Primitive
 Applied Optics
, 1990
"... The optical computing technology offers new challenges to the algorithm designers since it can perform an npoint DFT computation in only unit time. Note that DFT is a nontrivial computation in the PRAM model. We develop two new models, DFTVLSIO and DFTCircuit, to capture this characteristic of o ..."
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Cited by 12 (3 self)
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The optical computing technology offers new challenges to the algorithm designers since it can perform an npoint DFT computation in only unit time. Note that DFT is a nontrivial computation in the PRAM model. We develop two new models, DFTVLSIO and DFTCircuit, to capture this characteristic of optical computing. We also provide two paradigms for developing parallel algorithms in these models. Efficient parallel algorithms for many problems including polynomial and matrix computations, sorting and string matching are presented. The sorting and string matching algorithms are particularly noteworthy. Almost all of these algorithms are within a polylog factor of the optical computing (VLSIO) lower bounds derived in [BR87] and [TR90]. The research of J. Reif was supported in part by DARPA/ARO contract DAAL0388K0195, Air Force Contract AFOSR87 0386, DARPA/ISTO contract N0001488K0458, NASA subcontract 55063 of primecontract NAS530428. A. Tyagi was supported by NSF Grant #MIP8...
Computational Complexity of an Optical Model of Computation
, 2005
"... We investigate the computational complexity of an optically inspired model of computation. The model is called the continuous space machine and operates in discrete timesteps over a number of twodimensional complexvalued images of constant size and arbitrary spatial resolution. We define a number ..."
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Cited by 7 (7 self)
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We investigate the computational complexity of an optically inspired model of computation. The model is called the continuous space machine and operates in discrete timesteps over a number of twodimensional complexvalued images of constant size and arbitrary spatial resolution. We define a number of optically inspired complexity measures and data representations for the model. We show the growth of each complexity measure under each of the model's operations. We characterise the power of an important discrete restriction of the model. Parallel time on this variant of the model is shown to correspond, within a polynomial, to sequential space on Turing machines, thus verifying the parallel computation thesis. We also give a characterisation of the class NC. As a result the model has computational power equivalent to that of many wellknown parallel models. These characterisations give a method to translate parallel algorithms to optical algorithms and facilitate the application of the complexity theory toolbox to optical computers. Finally we show that another variation on the model is very powerful;
The traveling beam: optical solution for bounded NPcomplete problems
 The fourth international conference on fun with algorithms (FUN
, 2007
"... Architectures for optical processors designed to solve bounded instances of NPComplete problems are suggested. One approach mimics the traveling salesman by traveling beams that simultaneously examine the different possible paths. The other approach uses a preprocessing stage in which O(n 2) masks ..."
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Cited by 6 (3 self)
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Architectures for optical processors designed to solve bounded instances of NPComplete problems are suggested. One approach mimics the traveling salesman by traveling beams that simultaneously examine the different possible paths. The other approach uses a preprocessing stage in which O(n 2) masks are constructed, each representing a different edge in the graph. The choice and combination of the appropriate (small) subset of these masks yields the solution. The solution is rejected in cases where the combination of these masks totally blocks the light and accepted otherwise. We present detailed designs for basic primitives of the optical processor. We propose
Optical computing and computational complexity
 In Fifth International Conference on Unconventional Computation (UC’06), volume 4135 of LNCS
, 2006
"... 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 twodimensional images of fixed size and arbitrary spatial resolution. The ( ..."
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Cited by 3 (2 self)
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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 twodimensional 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 wellknown 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 tradeoffs. 1
Parallel and sequential optical computing
, 2008
"... We present a number of computational complexity results for an optical model of computation called the continuous space machine. We also describe an implementation for an optical computing algorithm that can be easily defined within the model. Our optical model is designed to model a wide class of ..."
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We present a number of computational complexity results for an optical model of computation called the continuous space machine. We also describe an implementation for an optical computing algorithm that can be easily defined within the model. Our optical model is designed to model a wide class of optical computers, such as matrix vector multipliers and pattern recognition architectures. It is known that the model solves intractable PSPACE problems in polynomial time, and NC problems in polylogarithmic time. Both of these results use large spatial resolution (number of pixels). Here we look at what happens when we have constant spatial resolution. It turns out that we obtain similar results by exploiting other resources, such as dynamic range and amplitude resolution. However, with certain other restrictions we essentially have a sequential device. Thus we are exploring the border between parallel and sequential computation in optical computing. We describe an optical architecture for the unordered search problem of finding a one in a list of zeros. We argue that our algorithm scales well, and is relatively straightforward to implement. This problem is easily parallelisable and is from the class NC. We go on to argue that the optical computing community should focus their attention on problems within P (and especially NC), rather than developing systems for tackling intractable problems. 1
Optical computing
, 2008
"... We consider optical computers that encode data using images and compute by transforming such images. We give an overview of a number of such optical computing architectures, including descriptions of the type of hardware commonly used in optical computing, as well as some of the computational effici ..."
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Cited by 3 (1 self)
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We consider optical computers that encode data using images and compute by transforming such images. We give an overview of a number of such optical computing architectures, including descriptions of the type of hardware commonly used in optical computing, as well as some of the computational efficiencies of optical devices. We go on to discuss optical computing from the point of view of computational complexity theory, with the aim of putting some old, and some very recent, results in context. Finally, we focus on a particular optical model of computation called the continuous space machine. We describe some results for this model including characterisations in terms of wellknown complexity classes.