Flat Splicing Array Grammar Systems Generating Picture Arrays

While studying the recombinant behaviour of DNA molecules, Head (1987) introduced a new operation, called splicing on words or strings, which are finite sequences of symbols. There has been intensive research using the concept of splicing on strings in the context of DNA computing, establishing important theoretical results on computational universality. A particular class of splicing, known as flat splicing on strings was recently considered and this operation was extended to provide picture array generating two-dimensional models. Making use of the operation of flat splicing on arrays, we propose here a grammar system, called flat splicing regular array grammar system (FSRAGS), as a new model of picture generation. The components of a FSRAGS generate picture arrays working in parallel using the rules of a two-phase grammar called 2RLG and with two different components of the FSRAGS communicating using the array flat splicing operations on columns and rows of the arrays. We establish some comparison results bringing out the generative power of FSRAGS and also exhibit the power of FSRAGS in generating certain “floor designs”

A Bio-inspired Model of Picture Array Generating P System with Restricted Insertion Rules

In the bio-inspired area of membrane computing, a novel computing model with a generic name of P system was introduced around the year 2000. Among its several variants, string or array language generating P systems involving rewriting rules have been considered. A new picture array model of array generating $P$ system with a restricted type of picture insertion rules and picture array objects in its regions, is introduced here. The generative power of such a system is investigated by comparing with the generative power of certain related picture array grammar models introduced and studied in two-dimensional picture language theory. It is shown that this new model of array P system can generate picture array languages which cannot be generated by many other array grammar models. The theoretical model developed is for handling the application problem of generation of patterns encoded as picture arrays over a finite set of symbols. As an application, certain floor-design patterns are generated using such an array $P$ system