A Study on Mathematical Model of n-th Order Limit Language from a Biological Perspective via Wet-Lab Experiment

The analysis of double-stranded DNA (dsDNA) recombinant behaviour led to the mathematical modelling of the deoxyribonucleic acid (DNA) splicing system. This multidisciplinary study is based on the fundamentals of formal language theory and informational macromolecules. The splicing system's number of rules previously specified the n-th order limit language. A previous experiment in the lab established the existence of a second-order limit language. Nevertheless, based on the quantity of rules employed in the splicing system, no laboratory experiments have been carried out to verify the existence of the n-th order limit language. This paper presents experimental evidence supporting the theoretical results of n-th order limit languages, which were previously proven using double induction. Laboratory experiments involving DNA digestion and ligation were conducted to validate these theoretical findings. This investigation has led to the validation of the model, indicating that research on third and fourth order limit language supports the notion of n-th order limit language biologically. Furthermore, it shows that the mathematical model of the n-th order limit language was empirically confirmed if the dsDNA molecules generated in the experiment match those anticipated by the model.This research advances the understanding of DNA splicing systems by empirically validating the n-th order limit language, bridging formal language theory and molecular biology, and paving the way for future studies and technological applications in DNA computing, synthetic biology, and bioinformatics.