2 research outputs found
Compositions of Functions and Permutations Specified by Minimal Reaction Systems
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.Comment: 10 pages, preprin
Ranks of Strictly Minimal Reaction Systems Induced by Permutations and Cartesian Product
Reaction system is a computing model inspired by the biochemical interaction
taking place within the living cells. Various extended or modified frameworks
motivated by biological, physical, or purely mathematically considerations have
been proposed and received significant amount of attention, notably in the
recent years. This study, however, takes after particular early works that
concentrated on the mathematical nature of minimal reaction systems in the
context-free basic framework and motivated by a recent result on the
sufficiency of strictly minimal reaction systems to simulate every reaction
system. This paper focuses on the largest reaction system rank attainable by
strictly minimal reaction systems, where the rank pertains to the minimum size
of a functionally equivalent reaction system. Precisely, we provide a very
detailed study for specific strictly minimal reaction system induced by
permutations, up to the quaternary alphabet. Along the way, we obtain a general
result about reaction system rank for Cartesian product of functions specified
by reaction systems.Comment: 18 pages, preprin