Set Turing Machines

TL;DR

This paper introduces a generalized Turing machine model that operates on arbitrary sets, demonstrating that its computable functions are equivalent to the class of Set Recursive functions, thus extending classical computability theory.

Contribution

It defines a new generalized Turing machine model and proves its computational power matches that of Set Recursive functions, bridging a gap in classical computability theory.

Findings

Generalized Turing machines compute exactly the Set Recursive functions

The class of computable functions remains unchanged under this generalization

Provides a new framework for understanding computation on arbitrary sets

Abstract

We define a generalization of the Turing machine that computes on general sets. Our main theorem states that the class of generalized Turing machine computable functions and the class of Set Recursive functions coincide.