Single-tape and multi-tape Turing machines through the lens of the Grossone methodology
Single-tape and multi-tape Turing machines through the lens of the Grossone methodology
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通过 Grossone 方法论的单带和多带图灵机
DOI：
10.1007/s11227-013-0894-y
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发表时间：
2013
期刊：
影响因子：
--
通讯作者：
A. Garro
中科院分区：
文献类型：
--
作者：
Y. Sergeyev;A. Garro
本文研究了用于描述和观察自动计算的数学语言如何影响所获得结果的准确性。我们特别将注意力集中在单带和多带图灵机上，它们是通过一种新的数学语言的镜头来描述和观察的，这种语言强烈地基于从物理学借用并应用于数学的三种方法论思想，即：观察的对象（我们在这里谈论数学对象）与用于该观察的仪器之间的区别；物体与观察工具之间的相互关系；由工具确定的观察的准确性。对传统语言和新语言执行的观察结果进行了比较和讨论。
The paper investigates how the mathematical languages used to describe and to observe automatic computations influence the accuracy of the obtained results. In particular, we focus our attention on single and multi-tape Turing machines, which are described and observed through the lens of a new mathematical language, which is strongly based on three methodological ideas borrowed from physics and applied to mathematics, namely: the distinction between the object (we speak here about a mathematical object) of an observation and the instrument used for this observation; interrelations holding between the object and the tool used for the observation; the accuracy of the observation determined by the tool. Results of the observation executed by the traditional and new languages are compared and discussed.