On Some Closure Properties of nc-eNCE Graph Grammars

In the study of automata and grammars, closure properties of the associated languages have been studied extensively. In particular, closure properties of various types of graph grammars have been examined in (Rozenberg and Welzl, Inf. and Control,1986) and (Rozenberg and Welzl, Acta Informatica,1986). In this paper we examine some critical closure properties of the nc-eNCE graph grammars discussed in (Jayakrishna and Mathew, Symmetry 2023) and (Jayakrishna and Mathew, ICMICDS 2022).Comment: 14 pages,9 figures, to be submitted to Theory of Computin

Spatial Existential Positive Logics for Hyperedge Replacement Grammars

We study a (first-order) spatial logic based on graphs of conjunctive queries for expressing (hyper-)graph languages. In this logic, each primitive positive (resp. existential positive) formula plays a role of an expression of a graph (resp. a finite language of graphs) modulo graph isomorphism. First, this paper presents a sound- and complete axiomatization for the equational theory of primitive/existential positive formulas under this spatial semantics. Second, we show Kleene theorems between this logic and hyperedge replacement grammars (HRGs), namely that over graphs, the class of existential positive first-order (resp. least fixpoint, transitive closure) formulas has the same expressive power as that of non-recursive (resp. all, linear) HRGs

A New Class of Graph Grammars and Modelling of Certain Biological Structures

Graph grammars can be used to model the development of diverse graph families. Since their creation in the late 1960s, graph grammars have found usage in a variety of fields, such as the design of sophisticated computer systems and electronic circuits, as well as visual languages, computer animation, and even the modelling of intricate molecular structures Replacement of edges and nodes are the two primary approaches of graph rewriting. In this paper we introduce a new type of node replacement graph grammar known as nc-eNCE graph grammar. With this new class of graph grammars we generated certain graph classes and we showed that these class of graph grammars are more powerful than the existing edge and node controlled embedding graph grammars. In addition, these graph grammars were used to model several common protein secondary structures such as parallel and anti-parallel b-sheet structures in different configurations. The use of these graph grammars in modelling other bio-chemical structures and their interactions remains to be explored

Interactive, tree-based graph visualization

We introduce an interactive graph visualization scheme that allows users to explore graphs by viewing them as a sequence of spanning trees, rather than the entire graph all at once. The user determines which spanning trees are displayed by selecting a vertex from the graph to be the root. Our main contributions are a graph drawing algorithm that generates meaningful representations of graphs using extracted spanning trees, and a graph animation algorithm for creating smooth, continuous transitions between graph drawings. We conduct experiments to measure how well our algorithms visualize graphs and compare them to another visualization scheme

Applications of an Agent-Based Approach to Automated Structure Design

This thesis details the applications of a new method of agent-based structure synthesis. The goal of this research is to create structures that meet a structural goal within a simulated physics environment. The method proposed works as an iterative process of changing the structure, evaluating the new structure and using this evaluation to inform the next change to the structure. Five example problems are used to elaborate the methods proposed in this research. Two are used to other compare this agent-based approach to other optimization methods and the remaining three show the ability of this method to develop emergent solutions