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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...
Evolution as a Computational Engine
 Proceedings of the Annual Conference of the European Association for Computer Science Logic
, 1997
"... this paper proves that for every computation problem, a set of lethal genes can be designed which steers the subsequent genome populations in a manner whereby the solution of the given computation problem will appear in the progeny. It is hardly likely that this observation will yield an application ..."
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Cited by 3 (0 self)
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this paper proves that for every computation problem, a set of lethal genes can be designed which steers the subsequent genome populations in a manner whereby the solution of the given computation problem will appear in the progeny. It is hardly likely that this observation will yield an application, but should nevertheless be mentioned. 1 Statement of results
A Random Walk in Statistical Physics
, 2001
"... This thesis deals with some aspects of the physics of disordered systems. It consists of four papers and an introductory part. An introduction ..."
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This thesis deals with some aspects of the physics of disordered systems. It consists of four papers and an introductory part. An introduction
A Computational View of Population Genetics (preliminary version)
, 1995
"... This paper contributes to the study of nonlinear dynamical systems from a computational perspective. These systems are inherently more powerful than their linear counterparts (such as Markov chains), which have had a wide impact in Computer Science, and they seem likely to play an increasing role in ..."
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This paper contributes to the study of nonlinear dynamical systems from a computational perspective. These systems are inherently more powerful than their linear counterparts (such as Markov chains), which have had a wide impact in Computer Science, and they seem likely to play an increasing role in future. However, there are as yet no general techniques available for handling the computational aspects of discrete nonlinear systems, and even the simplest examples seem very hard to analyze. We focus in this paper on a class of quadratic systems that are widely used as a model in population genetics and also in genetic algorithms. These systems describe a process where random matings occur between parental chromosomes via a mechanism known as "crossover": i.e., children inherit pieces of genetic material from different parents according to some random rule. Our results concern two fundamental quantitative properties of crossover systems: 1. We develop a general technique for computing th...
On the Power of BioComputers
, 1995
"... In [Adl94] Adleman used biological manipulations with DNA strings to solve some instances of the Directed Hamiltonian Path Problem. Lipton [Lip94] showed how to extend this idea to solve any NP problem. We prove that exactly the problems in P NP = \Delta p 2 can be solved in polynomial time using Li ..."
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In [Adl94] Adleman used biological manipulations with DNA strings to solve some instances of the Directed Hamiltonian Path Problem. Lipton [Lip94] showed how to extend this idea to solve any NP problem. We prove that exactly the problems in P NP = \Delta p 2 can be solved in polynomial time using Lipton's model. Various modifications of Lipton's model are investigated, and it is proved that their computational power in polynomial time can be characterized by one of the complexity classes P, \Delta p 2 , or \Delta p 3 . 1 Introduction In the last years several new ideas have been developed to use non electronic natural phenomena for real, efficient computation. In classical electronicbased computations the information is stored bitwise by electric and electromagnetic means, and the information is modified by using just these properties of the memory. It is typical for this kind of computations that the number of steps performed per time unit is huge but the number of processors r...
Yuval Rabani
"... This paper contributes to the study of nonlinear dynamical systems from a computational perspective. These systems are inherently more powerful than their linear counterparts (such as Markov chains), which have had a wide impact in Computer Science, and they seem likely to play an increasing role in ..."
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This paper contributes to the study of nonlinear dynamical systems from a computational perspective. These systems are inherently more powerful than their linear counterparts (such as Markov chains), which have had a wide impact in Computer Science, and they seem likely to play an increasing role in future. However, there are as yet no general techniques available for handling the computational aspects of discrete nonlinear systems, and even the simplest examples seem very hard to analyze. We focus in this paper on a class of quadratic systems that are widely used as a model in population genetics and also in genetic algorithms. These systems describe a process where random matings occur between parental chromosomes via a mechanism known as "crossover": i.e., children inherit pieces of genetic material from different parents according to some random rule. Our results concern two fundamental quantitative properties of crossover systems: 1. We develop a general technique for computing th...
Linear and NonLinear Systems: A Survey
"... . In this paper we present the research that has been done with Linear Dynamical Systems to generate almost uniformly elements from a given set, and thus approximate some hard counting problems. We also indicate how nonlinear systems can help to parallelize the computation. Finally we outline possi ..."
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. In this paper we present the research that has been done with Linear Dynamical Systems to generate almost uniformly elements from a given set, and thus approximate some hard counting problems. We also indicate how nonlinear systems can help to parallelize the computation. Finally we outline possible applications of linear systems to formalize heuristics. 1. Introduction Many problems involving counting solutions of combinatorial structures are well known to be difficult. Valiant defined the class #P of computationally equivalent counting problems ([Val79b]). For many problems in this class, their decision counterpart is in P . It is known that, unless the polynomial hierarchy collapses, P 6= #P . This fact implies that for any #P complete problem, exact counting is apparently intractable ([Pap94]). The most notorious of these problems is to compute the permanent of a dense matrix. That problem turns out to be equivalent to counting the number of perfect matchings in a dense bipar...