An accelerated Turing machine named a Zeno machine is a hypothetical computational model which can perform the countable infinite number of computational steps within a finite time. However, it cannot be physically realized from the standpoint of the Heisenberg uncertainty principle, because the energy required for the computation will be exponentially increased when the computational step is accelerated. In this article, we show the possibility to realize the Zeno machine by utilizing superluminal elementary particles instead of subliminal particles including photons, which leads to the realization of hypercomputational systems.