Increasing the computational power of n-th order limit languages up to context-sensitive language through grammar modifications

In previous research, the definition of the n-th order limit language, as introduced by Goode and Pixton, has been refined from a rule’s perspective. Initially, the n-th order limit language, denoted as Ln, involved the deletion of transient words in L_(n-1). Subsequent research extended this by emphasizing the quantity of initial strings and rules within the splicing system. However, these findings were derived from a splicing system model aimed at preserving biological splicing characteristics through the process of cutting and pasting genetic material (DNA) in the presence of restriction enzymes and ligase. This study shifts focus to a model based on the Chomsky hierarchy for language generation due to limitations in the biological-based model, which restricts language production to regular language only. Modifications were applied, such as varying the splicing system's variables, to adapt the definition to a widely used framework in language generation research, achieving a higher hierarchy of language production by the splicing system. Previously, the n-th order limit language was generalized using the biological-based splicing system, the Head splicing system S=(A,I,B,C) which was limited to the generation of languages to regular and context-free language only. To address this limitation, a revised definition of the n-th order limit language was formulated using the extended H splicing system γ=(V,T,Am,Rp), characterized by an infinite number of rules and axioms to extend the generation of language to context-free and context-sensitive by modifying grammar. This paper investigates how the new definition, based on the Păun splicing system, enhances the computational power of n-th order limit languages. By imposing a few restrictions and considering various cases, we aim to increase computational power. We have proved that the new definition increases the computational power of the languages produced by the extended H splicing system.