This paper presents a new approach to fractal image generation by translating the evolution of graph grammar into graphics output. It uses the algebraic approach of graph grammar as a powerful abstract modeling tool for the generation of selfsimilar fractal images via its graph production, derivations and double-pushout construction. We focus on three proposed methods for image generation which...

In [5] we introduced a framework for specification of parameterized data types utilizing a generalization of the traditional semantics based on the pushout construction. In the present paper, we address the issue of program development using this framework with particular emphasis on the notion of refinement. Unlike for the loose specifications, refinement does not amount merely to a narrowing ...

We show how evolution requests can be formalized using algebraic graph rewriting. In particular, we present a way to convert the UML class diagrams to colored graphs. Since changes in software may effect the relation between the methods of classes, our colored graph representation also employs the relations in UML interaction diagrams. Then, we provide a set of algebraic graph rewrite rules tha...

String diagrams are a powerful tool for reasoning about composite structures in symmetric monoidal categories. By representing string diagrams as graphs, equational reasoning can be done automatically by double-pushout rewriting. !-graphs give us the means of expressing and proving properties about whole families of these graphs simultaneously. While !-graphs provide elegant proofs of surprisin...

This paper describes methods for reducing the connectionless packet loss rate in the DQDB to ATM Interworking Unit (IWU). Results from simulation studies are presented to show the relationship between the buffering available in the IWU and the reduction in cell and packet loss probabilities. Further performance studies compare the performance of the Lost Packet Screening scheme, the Pushout Buf...

We obtain some explicit calculations of crossedQ-modules induced from a crossed module over a normal subgroup P of Q. By virtue of theorems of Brown and Higgins, this enables the computation of the homotopy 2-types and second homotopy modules of certain homotopy pushouts of maps of classifying spaces of discrete groups. Introduction A crossed module M = (μ : M → P ) has a classifying space BM (...

We present a mathematical model for the cognitive operation of conceptual blending that aims at being uniform across different representation formalisms, while capturing relevant structure this operation. The takes its inspiration from amalgams as applied in case-based reasoning, but lifts them into category theory so to follow Joseph Goguen’s intuition mathematically precise characterisation r...

Algebraic graph transformations visually support intuition, have a strong theoretical basis, and provide a formal, implementation independent basis for the description of discretely evolving computational systems and their formal and tractable analysis. Graph grammar models of concurrent systems (petri nets, actor systems) have inspired corresponding semantics developments. Recently this led to...

In a recent paper, mimicking Winskel’s construction for Petri nets, a concurrent semantics for (double-pushout) DPO graph grammars has been provided by showing that each graph grammar can be unfolded into an acyclic branching structure, that is itself a (nondeterministic occurrence) graph grammar describing all the possible computations of the original grammar. This paper faces the problem of p...