Array P systems were introduced by Paun Gh. which is linking the two areas of membrane computing and picture grammars. Puzzle grammars were introduced by us for generating connected picture arrays in the two-dimensional plane, motivated by the problem of tiling the plane. On the other hand, incorporating into arrays the developmental type of generation used in the well-known biologically motivated L systems, Siromoney and Siromoney proposed a very general rectangular array generating model, called extended controlled tabled L array system (ECTLAS). In this paper we introduce two variations of the array P system, called BPG array P system and parallel array P system. The former has in the regions array objects and basic puzzle grammar rules (BPG), which are a specific kind of puzzle grammar rules. In the latter, the regions have rectangular array objects and tables of context-free rules. We examine these two types of P systems for their array generative power.

Relating graph structures with words which are finite sequences of symbols, Parikh word representable graphs (PWRGs) were introduced. On the other hand, in chemical graph theory, graphs have been associated with molecular structures. Also, several topological indices have been defined in terms of graph parameters and studied for different classes of graphs. In this study, we derive expressions for computing certain topological indices of PWRGs of binary core words, thereby enriching the study of PWRGs.

The two areas of grammar systems and P systems, which have provided interesting computational models in the study of formal string language theory have been in the recent past effectively linked in [4] by incorporating into P systems, a communication mode called t–mode of cooperating distributed grammar systems. On the other hand cooperating array grammar systems [5] and array P systems [1] have been developed in the context of two-dimensional picture description. In this paper, motivated by the study of [4], these two systems are studied by linking them through the t–communication mode, thus bringing out the picture description power of these systems.