Some analysis on certain types of splicing systems

A mathematical model of a splicing system was firstly developed by Head in 1987. This model is abstractly analyzed in the framework of Formal Language Theory, which is a branch of Applied Discrete Mathematics and Theoretical Computer Science. This model consists of a finite set of initial strings over an alphabet that acts upon a finite set of rules. In this paper, some analysis on certain types of splicing systems namely, null-context, uniform, simple and S
k
H system are presented as propositions and corollaries. Besides, some counterexamples are given to illustrate these relations.