Sequential and graph controlled insertion-deletion systems

In this article, we consider a class of contextual insertion-deletion (Ins/Del) system on strings and languages. The notion of sequential operations to a given contextual insertion-deletion (Ins/Del) has been introduced for the first time. We found that sequential operation in contextual system characterizes non synchronized pure pattern language (NSPPL) and context free language (CFL). Moreover, a variant in the insertion-deletion system called graph controlled contextual insertion-deletion also enables to generate non synchronized pure pattern language which helps to improve the computational complexity.