论文标题
变体的跨限计算模型的特征：无限时间图丁，序数图和Blum-Shub-Smale机器
Characterisations of Variant Transfinite Computational Models: Infinite Time Turing, Ordinal Time Turing, and Blum-Shub-Smale machines
论文作者
论文摘要
我们考虑了转移机器体系结构的变化有时如何改变其功能。我们通过回答三个开放问题来解决该主题：首先，与单个头部，其次是空间需求以及最后限制规则相比，对具有多次倍数的机器的停止时间注意事项有所不同。我们：1）使用可接受性理论，$σ_{2} $ - 代码和$π_{3} $ - 构造层次结构中的反射属性，以对具有多个独立头部的ITTM的停止时间进行分类；对于具有$ \ tmop {on} $长度磁带的序着的图灵机的序数相同； 2）确定带有长磁带的转夹时间机的磁带长度，使机器可以解决其每个单元格 - B. Rin提出的问题； 3）准确地表征了使用$ \ tmop {liminf} $规则在其寄存器上进行的blum-shub-smale机器的强度和行为，从而确定有一个通用的机器。这与没有通用的“连续性”规则与机器相矛盾。
We consider how changes in transfinite machine architecture can sometimes alter substantially their capabilities. We approach the subject by answering three open problems touching on: firstly differing halting time considerations for machines with multiple as opposed to single heads, secondly space requirements, and lastly limit rules. We: 1) use admissibility theory, $Σ_{2}$-codes and $Π_{3}$-reflection properties in the constructible hierarchy to classify the halting times of ITTMs with multiple independent heads; the same for Ordinal Turing Machines which have $\tmop{On}$ length tapes; 2) determine which admissible lengths of tapes for transfinite time machines with long tapes allow the machine to address each of their cells - a question raised by B. Rin; 3) characterise exactly the strength and behaviour of transfinitely acting Blum-Shub-Smale machines using a $\tmop{Liminf}$ rule on their registers - thereby establishing there is a universal such machine. This is in contradistinction to the machine using a `continuity' rule which fails to be universal.
