Pure 2D picture grammars and languages

A new syntactic model, called pure two-dimensional (2D) context-free grammar (P2DCFG), is introduced based on the notion of pure context-free string grammar. The rectangular picture generative power of this 2D grammar model is investigated. Certain closure properties are obtained. An analogue of this 2D grammar model called pure 2D hexagonal context-free grammar (P2DHCFG) is also considered to generate hexagonal picture arrays on triangular grids

Array P Systems and t−Communication

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

Infinite arrays and infinite computations

AbstractA complete metric topology is introduced on the set of all finite and infinite arrays and the topological properties of the space are studied. In this complete metric topology, infinite arrays are the limits of increasing sequences of finite arrays. The notion of successful infinite derivations in Generalized Context-free Kolam Array Grammars, yielding infinite arrays, is a subclass of Generalized context-free kolam array grammars. For this class, the finite array language generated by a reduced grammar in Greibach normal form and the set of infinite arrays generated by it are related through the notion of adherence

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”

Solving 2D-pattern matching with networks of picture processors

We propose a solution based on networks of picture processors to the problem of picture pattern matching. The network solving the problem can be informally described as follows: it consists of two subnetworks, one of them extracts simultaneously all subpictures of the same size from the input picture and sends them to the second subnetwork. The second subnetwork checks whether any of the received pictures is identical to the pattern. We present an efficient solution based on networks with evolutionary processors only, for patterns with at most three rows or columns. Afterwards, we present a solution based on networks containing both evolutionary and hiding processors running in O(n+m+kl+k) computational (processing and communication) steps, where the input picture and the pattern are of size (n,m) and (k,l), respectively

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