We study the paradoxical aspects of closed time-like curves and their impact on the theory of computation. After introducing the $\text{TM}_\text{CTC}$, a classical Turing machine benefiting CTCs for backward time travel, Aaronson et al. proved that $\text{P} = \text{PSPACE}$ and the $\Delta_2$ sets, such as the halting problem, are computable within this computational model. Our critical view is the physical consistency of this model, which leads to proposing the strong axiom, explaining that every particle rounding on a CTC will be destroyed before returning to its starting time, and the weak axiom, describing the same notion, particularly for Turing machines. We claim that in a universe containing CTCs, the two axioms must be true; otherwise, there will be an infinite number of any particle rounding on a CTC in the universe. An immediate result of the weak axiom is the incapability of Turing machines to convey information for a full round on a CTC, leading to the proposed $\text{TM}_\text{CTC}$ programs for the aforementioned corollaries failing to function. We suggest our solution for this problem as the data transferring hypothesis, which applies another $\text{TM}_\text{CTC}$ as a means for storing data. A prerequisite for it is the existence of the concept of Turing machines throughout time, which makes it appear infeasible in our universe. Then, we discuss possible physical conditions that can be held for a universe containing CTCs and conclude that if returning to an approximately equivalent universe by a CTC was conceivable, the above corollaries would be valid.

翻译：我们研究了闭合类时曲线（CTC）的悖论性特征及其对计算理论的影响。在介绍了利用CTC实现时间回溯的经典图灵机模型$\text{TM}_\text{CTC}$后，Aaronson等人证明了在该计算模型下$\text{P} = \text{PSPACE}$且$\Delta_2$集合（如停机问题）是可计算的。我们对该模型的物理一致性持批判性观点，由此提出强公理（说明沿CTC循环的每个粒子将在返回起始时刻前被摧毁）和弱公理（针对图灵机描述相同概念）。我们断言：在包含CTC的宇宙中，这两个公理必然成立；否则宇宙中沿CTC循环的任意粒子将产生无限多个副本。弱公理的一个直接推论是：图灵机无法在完整CTC循环中传递信息，导致前述推论中提出的$\text{TM}_\text{CTC}$程序无法运行。针对该问题，我们提出数据传递假说作为解决方案，即利用另一台$\text{TM}_\text{CTC}$作为数据存储介质。其前提是图灵机概念需要贯穿时间维度始终，这使该方案在现实宇宙中难以实现。随后我们讨论了包含CTC的宇宙应满足的可能物理条件，并得出结论：若通过CTC返回近似等价宇宙的设想成立，则前述推论将是有效的。