A New Approach to Abstract Machines - Introduction to the Theory of Configuration Machines

TL;DR

This paper introduces configuration machines, a simple algebraic model for abstract machines, facilitating the study of their computational properties and universality, with a focus on primitive recursive functions and recursion theory.

Contribution

It formalizes the concept of configuration machines as an algebraic system, advancing the theoretical understanding of abstract machine models and their computational capabilities.

Findings

Configuration machines are formalized as algebraic systems.

Functions computed by primitive recursive configuration machines are recursive.

The theory aids in studying universal machines and their properties.

Abstract

An abstract machine is a theoretical model designed to perform a rigorous study of computation. Such a model usually consists of configurations, instructions, programs, inputs and outputs for the machine. In this paper we formalize these notions as a very simple algebraic system, called a configuration machine. If an abstract machine is defined as a configuration machine consisting of primitive recursive functions then the functions computed by the machine are always recursive. The theory of configuration machines provides a useful tool to study universal machines.