Zeno machines and Running Turing machine for infinite time

TL;DR

This paper examines the theoretical limits of Zeno machines and infinite-time Turing machine execution, establishing that the halting problem remains unsolvable regardless of infinite computation assumptions.

Contribution

It clarifies issues around Zeno machines and proves the impossibility of solving the halting problem through infinite-time Turing machine execution.

Findings

Halting problem cannot be solved using infinite-time Turing machines.

No physical bounds can justify solving the halting problem.

Zeno machines do not enable solving undecidable problems.

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.