Parallel contextual array insertion–deletion P systems and array rewriting P systems with pure 2D context-free rules

The problem of handling array languages using P systems was initially considered by Ceterchi et al. (In Nat Comput 2(3): 229–249, 2003), thereby linking the two areas of membrane computing and picture grammars. In recent years, the problem of the generation of 2D picture languages using P systems has received more attention James et al. (2017) introduced Parallel contextual array insertion–deletion P systems (PCAIDPS) exploiting insertion and deletion operations together with contextual operations. Subramanian et al. (In Math Comput Modell 152(2): 1901–1909, 2010) introduced the array-rewriting P system with pure 2D context-free rules AP(P2DCFG). In this paper, we compare the generative power of AP(P2DCFG) with that of PCAIDPS and prove that PCAIDPS has more generative power than that of AP(P2DCFG).