Compositions of Functions and Permutations Specified by Minimal Reaction Systems

TL;DR

This paper explores the mathematical properties of reaction systems, showing that functions specified by minimal reaction systems over a four-letter alphabet can generate the alternating group on the power set, highlighting their computational power.

Contribution

It extends previous work by analyzing the generative power of functions specified by minimal reaction systems, especially permutations, under composition.

Findings

Functions specified by minimal reaction systems can generate the alternating group.

Permutations over a quaternary alphabet are included in the generated group.

The study advances understanding of reaction systems' computational capabilities.

Abstract

This paper studies mathematical properties of reaction systems that was introduced by Enrenfeucht and Rozenberg as computational models inspired by biochemical reaction in the living cells. In particular, we continue the study on the generative power of functions specified by minimal reaction systems under composition initiated by Salomaa. Allowing degenerate reaction systems, functions specified by minimal reaction systems over a quarternary alphabet that are permutations generate the alternating group on the power set of the background set.