光线追踪-计算不可计算的?

Ed Blakey
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引用次数: 3

摘要

我们从以前的工作中回顾了计算复杂性理论的模型独立框架。值得注意的是,在本文中,该框架允许在考虑物理的、容易出错的(尤其是模拟的而不是数字的)计算系统时出现的精度问题的形式化。我们以光线追踪问题为例进行研究,这是一个图灵机无法计算的问题,尽管明显违反了丘奇-图灵论文,但据说可以由某些光学计算机解决;然而,我们应用复杂性理论的框架,以便形式化这种直觉,即一旦适当考虑精度,这些计算机的所谓超级图灵能力实际上就会消失。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
Ray tracing - computing the incomputable?
We recall from previous work a model-independent framework of computational complexity theory. Notably for the present paper, the framework allows formalization of the issues of precision that present themselves when one considers physical, error-prone (especially analogue rather than digital) computational systems. We take as a case study the ray-tracing problem, a Turing-machine-incomputable problem that can, in apparent violation of the Church-Turing thesis, nonetheless be said to be solved by certain optical computers; however, we apply the framework of complexity theory so as to formalize the intuition that the purported super-Turing power of these computers in fact vanishes once precision is properly considered.
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