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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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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.
What lies beyond the mountains? Computational systems beyond the Turing limit
 BULLETIN OF THE EUROPEAN ASSOCIATION FOR THEORETICAL COMPUTER SCIENCE
, 2005
"... Up to Turing power, all computations are describable by suitable programs, which correspond to the prescription by finite means of some rational parameters of the system or some computable reals. ¿From Turing power up we have computations that are not describable by finite means: computation without ..."
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Up to Turing power, all computations are describable by suitable programs, which correspond to the prescription by finite means of some rational parameters of the system or some computable reals. ¿From Turing power up we have computations that are not describable by finite means: computation without a program. When we observe natural phenomena and endow them with computational significance, it is not the algorithm we are observing but the process. Some objects near us may be performing hypercomputation: we observe them, but we will never be able to simulate their behaviour on a computer. What is then the profit of such a theory of computation to Science?
Large Scale Simulations of Complex Systems Part I: Conceptual Framework
, 1997
"... In this working document, we report on a new approach to high performance simulation. The main inspiration to this approach is the concept of complex systems: disparate elements with well defined interactions rules and non nonlinear emergent macroscopic behavior. We provide arguments and mechanisms ..."
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In this working document, we report on a new approach to high performance simulation. The main inspiration to this approach is the concept of complex systems: disparate elements with well defined interactions rules and non nonlinear emergent macroscopic behavior. We provide arguments and mechanisms to abstract temporal and spatial locality from the application and to incorporate this locality into the complete design cycle of modeling and simulation on parallel architectures. Although the main application area discussed here is physics, the presented Virtual Particle (VIP) paradigm in the context of Dynamic Complex Systems (DCS), is applicable to other areas of compute intensive applications. Part I deals with the concepts behind the VIP and DCS models. A formal approach to the mapping of application taskgraphs to machine taskgraphs is presented. The major part of section 3 has recently (July 1997) been accepted for publication in Complexity. In Part II we will elaborate on the execution behavior of