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19
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 29 (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 13 (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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Cited by 3 (1 self)
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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 Waveguides in General Purpose Parallel Computers
, 1992
"... this memory line are updated, and the line is returned to the requesting cache. The updatebit in the cache line's directory entry is also set to indicate that the requested should be kept up to date. When the READUPDATE command is issued and the data is present in the cache, then the cache can imm ..."
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Cited by 2 (2 self)
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this memory line are updated, and the line is returned to the requesting cache. The updatebit in the cache line's directory entry is also set to indicate that the requested should be kept up to date. When the READUPDATE command is issued and the data is present in the cache, then the cache can immediately return the value to the CPU as a local operation. The RESETUPDATE command allows the node to clear the updatebit in that cache line's directory entry. When that bit is cleared, this signifies that the node is no longer interested in maintaining the coherence of that line. The cache line's directory entry is also removed from the doubly linked list. The updatebit is also cleared when the cache line must be replaced, and the directory entry is removed from the chain. The WRITEUPDATE command is used to update shared data and propagate the change to interested nodes. The write is placed into the node's Write Buffer (as shown in Fig. 4). From the node's viewpoint, the update has now occurred. The Write Buffer, through the Network Controller, sends out the update to the appropriate memory module when it can gain access to the network. The memory module then uses the chain to send the updated value out to all caches which want the updated value. Thus, the updates are sent in a pointtopoint fashion as each cache receives the updated value and passes it to the next one in the chain. The reader will recall from the discussion in Section 2.2 that a task reaches the end of its Synchronization Epoch (SE) when the CPSynch (Consistency Preserving) point is encountered. Although the task considers WRITEUPDATEs to be finished, while in its SE, after issuing the command, when the task reaches the CPSynch point, the task must issue the FLUSHBUFFER command in order to obey t...
Connectionist Learning Architecture Based on an Optical ThinFilm Multilayer Model
, 1997
"... Connectionist models consist of large numbers of simple but highly interconnected "units". They represent an approach that is quite different from that of classical models based on the structure of Von Neumann machines. Although the term "connectionist models" often refers to artificial neural netwo ..."
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Cited by 2 (2 self)
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Connectionist models consist of large numbers of simple but highly interconnected "units". They represent an approach that is quite different from that of classical models based on the structure of Von Neumann machines. Although the term "connectionist models" often refers to artificial neural network models, which are inspired directly by the biological neurons, there are also other connectionist architectures that differ significantly from this biological exemplar. This thesis describes such a "novel" connectionist learning architecture based on the technology of optical thinfilm multilayer. The proposed connectionist model consists of multiple thinfilm layers (similar to simple processing units in a neural network model), each with different refractive index and thickness. A light beam incident perpendicular to the surface of the multilayer stack is used to carry out the required computation. The reflectance of the light incident can be used as the general measurement of the outputs. Inputs can be fed into the system by encoding them into some system parameters such as refractive indices, and individual layer thicknesses can be used as adjustable parameters that are equivalent to the connection weights of a neural network model. Since this approach involves optical signal processing, the proposed connectionist learning architecture has unique properties and could offer significant advantages. Much of the work has focused on developing this new connectionist learning architecture and investigating its capability to accomplish complex computational tasks which have been extensively studied for conventional connectionist models such as the widely used feedforward neural network using the backpropagation learning by gradient descent. A prototype simulation model ha...