Array-Rewriting P Systems with Basic Puzzle Grammar Rules and Permitting Features

Abstract

Motivated by the problem of tiling the plane, puzzle grammars were introduced as a mechanism for generating languages of picture arrays in the two-dimensional plane. On the other hand BPG array P system with array objects and basic puzzle grammar (BPG) rules was introduced as a variant of array generating P systems that were developed with a view to link the two areas of membrane computing and picture array grammars. Here we incorporate the feature of permitting symbols in the rules of the BPG array P system, thus introducing permitting array P system with BPG rules (pAP(BPG)). We show that the permitting feature gives more generative power to the BPG array P system with one or two membranes. We also show that a pAP(BPG) with only two membranes under t–communication mode, can generate picture arrays of square frames.