Some Considerations on Universality

TL;DR

This paper discusses the concept of universality beyond Turing computability, exploring whether universal structures exist for non-Turing-computable systems and examining constructions of universal machines.

Contribution

It analyzes the possibility of universal structures in non-Turing frameworks and details constructions of universal Turing machines with constraints.

Findings

Universal Turing machines are constructed and analyzed.

Existence of universal structures in non-Turing systems is discussed.

Constraints on universal machines are examined.

Abstract

The paper puts into discussion the concept of universality, in particular for structures not of the power of Turing computability. The question arises if for such structures a universal structure of the same kind exists or not. For that the construction of universal Turing machines and those with some constraints are presented in some detail.