Zeno machines and Running Turing machine for infinite time

Abstract

This paper explores and clarifies several issues surrounding Zeno machines and the issue of running a Turing machine for infinite time. Without a minimum hypothetical bound on physical conditions, any magical machine can be created, and therefore, a thesis on the bound is formulated. This paper then proves that the halting problem algorithm for every Turing-recognizable program and every input cannot be devised whatever method is used to exploit infinite running-time of Turing machine.