论表示与可计算性的关系
On the relation between representations and computability
摘要：
可计算性的一个基本结果是存在无法计算的定义良好的函数。在本文中，我们研究的数据表示对可计算性的影响，我们表明，虽然每一种可能的方式表示数据存在不可计算的功能，一个特定的抽象函数的可计算性从来不是一个绝对的属性，但取决于用于功能域的表示。我们研究这种依赖关系的范围，并提供数学标准，有利于一些表示超过其他人。正如我们将要展示的，有很强的理由表明，计算可枚举性应该是计算模型的一个附加公理。我们分析的技术和代表性的变化和甲骨文机器的影响之间的联系，显示其层次结构之间的重要联系。最后，这些概念使我们能够获得一个新的洞察丘奇图灵命题：它的解释为计算是不变的基本代数结构。
英文摘要：
One of the fundamental results in computability is the existence of well-defined functions that cannot be computed. In this paper we study the effects of data representation on computability; we show that, while for each possible way of representing data there exist incomputable functions, the computability of a specific abstract function is never an absolute property, but depends on the representation used for the function domain. We examine the scope of this dependency and provide mathematical criteria to favour some representations over others. As we shall show, there are strong reasons to suggest that computational enumerability should be an additional axiom for computation models. We analyze the link between the techniques and effects of representation changes and those of oracle machines, showing an important connection between their hierarchies. Finally, these notions enable us to gain a new insight on the Church-Turing thesis: its interpretation as the underlying algebraic structure to which computation is invariant.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
