Hypercomputation: Towards an extension of the classical notion of Computability?

TL;DR

This thesis explores hypercomputation, analyzing its theoretical foundations, physical realizability, and connections to quantum computing, aiming to extend classical notions of computability.

Contribution

It provides a comprehensive analysis of hypercomputation, hypermachines, and their potential physical implementations, including a preliminary look at quantum hypercomputational models.

Findings

Hypercomputation extends classical computability concepts.

Physical realization of hypermachines remains speculative.

Quantum models like Kieu's Adiabatic Quantum Computing offer potential hypercomputational capabilities.

Abstract

The purpose of this thesis is to make an analysis of the concept of Hypercomputation and of some hypermachines. This thesis is separated in three main parts. We start in the first chapter with an analysis of the concept of Classical Computability with the Turing Machine and the Church-Turing thesis as a main reference and afterwards, in the second chapter, we continue with an analysis of hypercomputation and some hypermachines. Attention is given to the possible physical realization of these machines and their usefulness. In the third chapter a superficial introduction to Quantum Computing is made and a brief analysis to a quantum hypercomputational model, Tien D. Kieu's Adiabatic Quantum Computing.