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The complexity of analog computation
 in Math. and Computers in Simulation 28(1986
"... We ask if analog computers can solve NPcomplete problems efficiently. Regarding this as unlikely, we formulate a strong version of Church’s Thesis: that any analog computer can be simulated efficiently (in polynomial time) by a digital computer. From this assumption and the assumption that P ≠ NP w ..."
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Cited by 38 (0 self)
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We ask if analog computers can solve NPcomplete problems efficiently. Regarding this as unlikely, we formulate a strong version of Church’s Thesis: that any analog computer can be simulated efficiently (in polynomial time) by a digital computer. From this assumption and the assumption that P ≠ NP we can draw conclusions about the operation of physical devices used for computation. An NPcomplete problem, 3SAT, is reduced to the problem of checking whether a feasible point is a local optimum of an optimization problem. A mechanical device is proposed for the solution of this problem. It encodes variables as shaft angles and uses gears and smooth cams. If we grant Strong Church’s Thesis, that P ≠ NP, and a certain ‘‘Downhill Principle’ ’ governing the physical behavior of the machine, we conclude that it cannot operate successfully while using only polynomial resources. We next prove Strong Church’s Thesis for a class of analog computers described by wellbehaved ordinary differential equations, which we can take as representing part of classical mechanics. We conclude with a comment on the recently discovered connection between spin glasses and combinatorial optimization. 1.
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...
An Analog Model of Computation for the IllPosed Problems of Early Vision
 Artificial Intelligence Lab. Memo
, 1984
"... this paper, we suggest an analog model of computation in electrical or chemical netwo'ks for a I[trge class of vision problems, that maps more easily into biologically plausible mechanisms. Poggio and Torre (1984) have recently recognized that early vision problems such as motion analysis (!lorn an ..."
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Cited by 4 (2 self)
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this paper, we suggest an analog model of computation in electrical or chemical netwo'ks for a I[trge class of vision problems, that maps more easily into biologically plausible mechanisms. Poggio and Torre (1984) have recently recognized that early vision problems such as motion analysis (!lorn and Schunck, '19S1; Hildreth, 1984a,b), edge detection ('Forre and Poggio, 1984), surface interpolation (Grimson, 1981; Terzopoulos 1984), shapefromshading (Ikeuchi and Horn, '1981) and stereoms. tching can be characterized as m,.qthematica!ly illposed problems in tte sense of Hadamard (1923). Illposed problems can be "solved", according to re.quttrization theories, by variational principles of a specific type. A natural way of implementing variational problems are electrical, chemical or neuronal networks. We present specific networks for solving several lowlevel vision problems, SLch as the computation ol visual motion and edge detection
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"... Abstract: I offer an explication of the notion of the computer, grounded in the practices of computability theorists and computer scientists. I begin by explaining what distinguishes computers from calculators. Then, I offer a systematic taxonomy of kinds of computer, including hardwired versus pro ..."
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Abstract: I offer an explication of the notion of the computer, grounded in the practices of computability theorists and computer scientists. I begin by explaining what distinguishes computers from calculators. Then, I offer a systematic taxonomy of kinds of computer, including hardwired versus programmable, generalpurpose versus specialpurpose, analog versus digital, and serial versus parallel, giving explicit criteria for each kind. My account is mechanistic: which class a system belongs in, and which functions are computable by which system, depends on the system’s mechanistic properties. Finally, I briefly illustrate how my account sheds light on some issues in the history and philosophy of computing as well as the philosophy of mind. What exactly is a digital computer? (Searle, 1992, p. 205) In our everyday life, we distinguish between things that compute, such as pocket calculators, and things that don’t, such as bicycles. We also distinguish between different kinds of computing device. Some devices, such as abaci,
Optimized Mains Filter for Grid Connected Solar Power Inverter
"... Abstract: Conventional structures of power inverter filters, required for grid coupling operation and to fulfill EMI requirements, lead to a system, which was difficult to control (due to its high system order) and problematic to realize due to unknown mains impedance behavior. In this paper, a mat ..."
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Abstract: Conventional structures of power inverter filters, required for grid coupling operation and to fulfill EMI requirements, lead to a system, which was difficult to control (due to its high system order) and problematic to realize due to unknown mains impedance behavior. In this paper, a matching filter topology is presented, which can overcome all these limitations. It is shown, that the optimal adaptation of the presented structure leads to a simple, insensitive, easy to use and very robust solution. KeyWords: solar power inverter, gridconnected, mains filter 1