  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.
