A Continuous Model of Computation
نویسنده
چکیده
Although the Turing-machine model of computation is widely used in computer science it is fundamentally inadequate as a foundation for the theory of modern scientific computation. The real-number model is described as an alternative. Physicists often choose continuous mathematical models for problems ranging from the dynamical systems of classical physics to the operator equations and path integrals of quantum mechanics.These mathematical models use the real or complex number fields and we argue that the real-number model of computation should be used in the study of the computational complexity of continuous mathematical models. The study of continuous complexity is called information-based complexity. In this expository article we apply information-based complexity to topics such as breaking the curse of dimensionality, approximating the calculation of path integrals, and solving ill-posed problems. Precise formulations of these ideas may be found in J. F. Traub and A. G. Werschulz, “Complexity and Information”, Cambridge University Press, 1998. A central dogma of computer science is that the Turing machine model is the appropriate abstraction of a digital computer. Physicists who’ve thought about this also seem to favor the Turing machine model. For example, Roger Penrose [1] devotes some 60 pages to a description of this abstract model of computation and its implications. I will argue that physicists should consider the real-number model of computation as more appropriate and useful for scientific computation.ion of a digital computer. Physicists who’ve thought about this also seem to favor the Turing machine model. For example, Roger Penrose [1] devotes some 60 pages to a description of this abstract model of computation and its implications. I will argue that physicists should consider the real-number model of computation as more appropriate and useful for scientific computation. First, I’ll introduce the four “worlds” that will play a role; see Figure 1. Above the horizontal line are two real worlds; the world of physical phenomena and the computer world, where simulations are performed. Below the horizontal line are two formal worlds; a mathematical model of the physical phenomenon and a model of computation which is an
منابع مشابه
A duality between LM-fuzzy possibility computations and their logical semantics
Let X be a dcpo and let L be a complete lattice. The family σL(X) of all Scott continuous mappings from X to L is a complete lattice under pointwise order, we call it the L-fuzzy Scott structure on X. Let E be a dcpo. A mapping g : σL(E) −> M is called an LM-fuzzy possibility valuation of E if it preserves arbitrary unions. Denote by πLM(E) the set of all LM-fuzzy possibility valuations of E. T...
متن کاملA New Continuous Multi-State Reliability Model with Time Dependent Component Performance Rate
A CSS1†is a system with the continues-state components. When a component has the ability to obtain all the situations from completely working to completely failed, it named continues-state component. In the real world, performance rate of elements are continuous and decrease by time. Continuity of components causes infinite working states and grows up the system states. In this paper we propose...
متن کاملMHIDCA: Multi Level Hybrid Intrusion Detection and Continuous Authentication for MANET Security
Mobile ad-hoc networks have attracted a great deal of attentions over the past few years. Considering their applications, the security issue has a great significance in them. Security scheme utilization that includes prevention and detection has the worth of consideration. In this paper, a method is presented that includes a multi-level security scheme to identify intrusion by sensors and authe...
متن کاملمدلسازی حذف الکترومغناطیسی آخال به صورت پیوسته از مذاب فلزات
In this research, a 3-D mathematical model is developed for simulating electromagnetic continuous removal of inclusions from molten metals. The model includes the computation of electromagnetic force field and fluid flow in the presence of electromagnetic forces. The results of flow field together with electromagnetic force field were further used for calculating the trajectory of inc...
متن کاملA one-model approach for Computation of congestion With productions trade-offs and weight restrictions
متن کامل
A New Approach for Approximating Solution of Continuous Semi-Infinite Linear Programming
This paper describes a new optimization method for solving continuous semi-infinite linear problems. With regard to the dual properties, the problem is presented as a measure theoretical optimization problem, in which the existence of the solution is guaranteed. Then, on the basis of the atomic measure properties, a computation method was presented for obtaining the near optimal so...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
- CoRR
دوره physics/0106045 شماره
صفحات -
تاریخ انتشار 1998