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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...
Analog Computation with Dynamical Systems
 Physica D
, 1997
"... This paper presents a theory that enables to interpret natural processes as special purpose analog computers. Since physical systems are naturally described in continuous time, a definition of computational complexity for continuous time systems is required. In analogy with the classical discrete th ..."
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Cited by 21 (0 self)
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This paper presents a theory that enables to interpret natural processes as special purpose analog computers. Since physical systems are naturally described in continuous time, a definition of computational complexity for continuous time systems is required. In analogy with the classical discrete theory we develop fundamentals of computational complexity for dynamical systems, discrete or continuous in time, on the basis of an intrinsic time scale of the system. Dissipative dynamical systems are classified into the computational complexity classes P d , CoRP d , NP d
Analog computation with dynamical systems
"... A b s t r a c t Physical systems exhibit various levels of complexity: their long term dynamics may converge to fixed points or exhibit complex chaotic behavior. This paper presents a theory that enables to interpret natural processes as special purpose analog computers. Since physical systems are n ..."
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A b s t r a c t Physical systems exhibit various levels of complexity: their long term dynamics may converge to fixed points or exhibit complex chaotic behavior. This paper presents a theory that enables to interpret natural processes as special purpose analog computers. Since physical systems are naturally described in continuous time, a definition of computational complexity for continuous time systems is required. In analogy with the classical discrete theory we develop fundamentals of computational complexity for dynamical systems, discrete or continuous in time, on the basis of an intrinsic time scale of the system. Dissipative dynamical systems are classified into the computational complexity classes Pd, CoRPd, NPd and EXP,t, corresponding to their standard counterparts, according to the complexity of their long term behavior. The complexity of chaotic attractors relative to regular ones leads to the conjecture Pa:fi NPj. Continuous time flows have been proven useful in solving various practical problems. Our theory provides the tools for an algorithmic analysis of such flows. As an example we analyze the