Zeno machines and hypercomputation

TL;DR

This paper reviews the Church-Turing Thesis and explores hypercomputational models like Zeno machines, discussing their implications for the limits of computation and the halting problem.

Contribution

It provides a comprehensive review of hypercomputation models, especially Zeno machines, and discusses their relation to classical computability and the halting problem.

Findings

Zeno machines are a straightforward hypercomputational model.

The halting problem remains a fundamental limitation across models.

Claims of surpassing Turing computability are viewed with skepticism.

Abstract

This paper reviews the Church-Turing Thesis (or rather, theses) with reference to their origin and application and considers some models of "hypercomputation", concentrating on perhaps the most straight-forward option: Zeno machines (Turing machines with accelerating clock). The halting problem is briefly discussed in a general context and the suggestion that it is an inevitable companion of any reasonable computational model is emphasised. It is hinted that claims to have "broken the Turing barrier" could be toned down and that the important and well-founded role of Turing computability in the mathematical sciences stands unchallenged.