T. Kamaraj’s research while affiliated with Sathyabama Institute of Science and Technology and other places

Ecosystems are extraordinarily complex assemblages of plants and animals interacting with each other, with the physical environment, and, increasingly, with humans. Ecology is the scientific field that seeks to understand ecosystems. Ecologists are turning to computer models to help them make their models of ecosystem processes concrete and to provide predictions about the future of the ecosystem. Computer models allow rapid testing of ecology ideas by simulation and provide the means to run "what-if" scenarios that would be difficult or impossible otherwise. Petri Net Generating Triangular Arrays were introduced by Kuberal et al. (2015) to generate Triangular Arrays using Petri Net structure. A new model to generate Octagonal Arrays using Petri Net Structure has been defined and it is proved that this model generate Octagonal Array Languages. The catenation of an arrowhead to a b-octagon results in a similar b-octagon. This concept has been used in Octagonal Array Token Petri Net Structure (OATPNS).

Hexagonal Prusa grammar (hex-PG) is an appealing version of Prusa grammar model proposed recently for generating hexagonal picture patterns. This model features the hexagonal context-free derivation rules in parallel application mode. It has been already proved that the class of languages generated by hex-PG includes that of classical context-free hexagonal array grammars and is included in a recent class of languages generated by regional hexagonal tile rewriting grammars. In this paper, we study the expressive power of hex-PG by comparing it with other existing hexagonal array generating grammars involving parallel rewriting rules.

Octagonal Tile Rewriting Grammars are modern class of octagonal tiling based Array Rewriting Grammar models on picture processing. They form the octagonal variant of triangular (hexagonal) Tile rewriting Grammars. We introduce Regional Octagonal Tile Rewriting Grammar (ROTRG) and generate images. We have compared this model with Context Free Octagonal Array Grammar and Octagonal Tile Rewriting Grammar.

Triangular Tile Rewriting Grammars (TTRG) are the recent class of formal modelsfor the generation of triangular picture languages. They combined the features of triangular tiling system (TTS) and array rewriting. Regional hexagonal tile rewriting grammars are the hexagonal array generating devices which employ replacement rules formalized by regional hexagonal tiling. In this work we introduce Regional Triangular Tile Rewriting Grammars (RTTRG) for the generation of triangular picture patterns. We compare this model with context free triangular array grammars, TTS and TTRG.

Tile Rewriting Grammars (TRG) are a new model for defining picture languages introduced in [1,7]. A rewriting rule changes a homogeneous rectangular sub-picture into an isometric one tiled with specified tiles[2]. Derivation and language generation with TRG rules are similar to context-free grammars. F. Sweety et al [4,10] have introduced Hexagonal Tile Rewriting Grammars (HTRG). Kuberal. S et al [13] have introduced Triangular Tile Rewriting Grammars and Triangular Picture Languages (TTRG). In this chapter we propose Octagonal Tile Rewriting Grammars (OTRG) for generating Octagonal Picture Languages. OTRG is the extension of HTRG and TTRG. We study the derivation of OTRG and also language generation with OTRG rules. Some closure properties are studied. OTRG is also compared with OLOC and OLOCu,eq. INTRODUCTION A picture is a rectangular array of terminal symbols (the pixels). A survey of formal models for picture languages is [3] where different approaches are compared and related: tiling systems, cellular automata and grammars. Classical 2D grammars can be grouped into two categories called matrix and array grammars. The matrix grammars introduced by A. Rosenfeld [11], impose the constraint that the left and right parts of a rewriting rule must be isometric arrays; this condition overcomes the inherent problem of "shearing" which pops up while substituting a sub-array in a host array. Siromoney'sarray grammars [3] are parallel-sequential in nature, in the sense that first a horizontal string of non-terminals is derived sequentially, using the horizontal production; and then the vertical derivations proceed in parallel, applying a set of vertical productions. A TRG rule is a schema having to the left a non-terminal symbol and to the right a local 2D language over terminals and non-terminals; that is the right part is specified by a set of fixed size tiles. As in matrix grammars, the shearing problem is avoided by an isometric constraint but the size of a TRG rule needs not to be fixed. The left part denotes any rectangle filled with the same non-terminal. Whatever size the left part takes, the same size is assigned to the right part. To make this idea effective, we impose a tree partial order on the areas which are rewritten. A progressively refined equivalence relation implements the partial ordering. Derivations can then be visualized in 3D as well nested prisms, the analogue of syntax trees on string grammars. Using TTRG rules, we can generated languages and pictures [13]. In this paper we propose Octagonal tile rewriting grammars using Octagonal tiles. We also study some closure properties of it. It is compared with other models.

A new model to generate triangular arrays using petri net structure has been defined. The catenation of an arrowhead to an equilateral triangle results in a similar equilateral triangle. This concept has been used in Triangular Array Token Petri Net Structure (TATPNS). Comparisons with other triangular array models have been made.

The concept of partial commutation and traces on strings has been recently extended to rectangular picture arrays and languages, motivated by the two-dimensional patterns which appear in studies concerning parallel computing and image analysis. The closure property of Siromoney matrix languages (SML) under partial commutation is already studied. In this paper, we consider partial commutation on a generalization of SML languages and Siromoney array languages (SAG) and establish some interesting results. Also, we examine the partial commutativity applied on some higher classes of 2D picture languages generated by Regional tile rewriting grammars and Prusa grammars. We extend partial commutation concept to hexagonal pictures also.

Prusa Grammar is a recently introduced rectangular picture languages generating model which exploits the parallel application of two-dimensional context-free rules. We introduce the hexagonal version of Prusa grammar and generate images. We compare this model with other hexagonal array generating devices for the description of its generative power.

Adjunct array token Petri net structure (AATPNS) is a recently introduced rectangular picture generating device which extends Array token Petri net structure. AATPNS generates some of the classical classes of picture languages namely Siromoney matrix languages and kolam array languages, and a recent, pure 2D context-free languages. In this paper we concentrate our attention on determining the generative power of AATPNS by comparing it with some expressive rectangular picture grammar models and also with the classes of languages recognizable by tiling systems. We also study certain closure properties with respect to basic array operations.