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.
Highlights
Living nature demonstrates how to program discrete spatiotemporal systems: It generates chains of amino acids from genetic code [1]
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
Summary
Living nature demonstrates how to program discrete spatiotemporal systems: It generates chains of amino acids from genetic code [1]. Abstracting a discrete physical system, for instance a computer, from its metrics, i.e. from the spatial measures of its components, the residue is a three-dimensional directed network of the executable functions which are realized by the components. The first set of production rules introduces an AA language for the abstract description of planar and antiparallel structures, the second set extends the AA language to represent symbolic networks, the third one extends it to describe digital or analog functional structures, and the fourth one to even comprise metric structures. In order to expand AA into a metric language requires the extension of Akton sorts and Interface sorts For this purpose, several basic geometrical structures need to be introduced as for instance multiple links, multiple forks, multiple joins as well as topological cuts.
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