Turing computability is the standard computability paradigm which captures the computational power of digital computers. To understand whether one can create physically realistic devices which have super-Turing power, one needs to understand whether it is possible to obtain systems with super-Turing capabilities which also have other desirable properties such as robustness to perturbations. In this paper we introduce a framework for analyzing whether a non-computability result is robust over continuous spaces. Then we use this framework to study the degree of robustness of several non-computability results which involve the wave equation, differentiation, and basins of attraction.
翻译:图图计算是标准计算模式,它捕捉了数字计算机的计算能力。为了了解人们是否能够创建具有超级试验能力的符合实际现实的装置,人们需要了解是否有可能获得具有超级试验能力的系统,这些系统还具有其他可取的特性,如振动的坚固性。在本文件中,我们引入了一个框架,用于分析非计算性结果是否对连续空间具有强健性。然后,我们利用这个框架来研究若干非计算性结果的稳健性程度,这些结果涉及波方程、差异和吸引力盆地。