Programming Discrete Physical Systems

TL;DR

This paper introduces Akton-Algebra, a programming language designed to describe and construct discrete physical systems by representing their topological networks, enabling automatic system description and hardware construction.

Contribution

It presents a novel language, Akton-Algebra, that unifies the description, programming, and hardware construction of discrete physical systems based on their topological networks.

Findings

Akton-Algebra can represent any discrete physical system as a topological network.

The language can be transformed into classical programming languages with clock control and addressing.

It enables automatic description and construction of complex physical systems.

Abstract

Every algorithm which can be executed on a computer can at least in principle be realized in hardware, i.e. by a discrete physical system. The problem is that up to now there is no programming language by which physical systems can constructively be described. Such tool, however, is essential for the compact description and automatic production of complex systems. This paper introduces a programming language, called Akton-Algebra, which provides the foundation for the complete description of discrete physical systems. The approach originates from the finding that every discrete physical system reduces to a spatiotemporal topological network of nodes, if the functional and metric properties are deleted. A next finding is that there exists a homeomorphism between the topological network and a sequence of symbols representing a program by which the original nodal network can be reconstructed. Providing Akton-Algebra with functionality turns it into a flow-controlled general data processing language, which by introducing clock control and addressing can be further transformed into a classical programming language. Providing Akton-Algebra with metrics, i.e. the shape and size of the components, turns it into a novel hardware system construction language.