Frank Drewes

Tree-based picture generation

The concept of tree-based picture generation is introduced. It is shown that there are equivalent tree-based definitions of four picture-generating devices known from the literature, namely collage ...

Hierarchical Graph Transformation

We present an approach for the rule-based transformation of hierarchically structured (hyper)graphs. In these graphs, distinguished hyperedges contain graphs that can be hierarchical again. Our framework extends the double-pushout approach from flat to hierarchical graphs. In particular, we show how to construct recursively pushouts and pushout complements of hierarchical graphs and graph morphisms. To further enhance the expressiveness of the approach, we also introduce rule schemata with variables which allow to copy and to remove hierarchical subgraphs.

Adaptive star grammars

We propose an extension of node and hyperedge replacement grammars, called adaptive star grammars, and study their basic properties. A rule in an adaptive star grammar is actually a rule schema which, via the so-called cloning operation, yields a potentially infinite number of concrete rules. Adaptive star grammars are motivated by application areas such as modeling and refactoring object-oriented programs. We prove that cloning can be applied lazily. Unrestricted adaptive star grammars are shown to be capable of generating every type-0 string language. However, we identify a reasonably large subclass for which the membership problem is decidable.

A Note on Hyperedge Replacement

In this note, we recall the basic features of hyperedge replacement as one of the most elementary and frequently used concepts of graph rewriting. Moreover, we discuss the Contextfreeness Lemma for derivations in hyperedge-replacement grammars.

Shaped Generic Graph Transformation

Since the systematic evolution of graph-like program models has become important in software engineering, graph transformation has gained much attention in this area. For specifying model evolution concisely, graph transformation rules should be as expressive as possible. The generic rules proposed in this paper may contain placeholders for graphs of varying number and shape. Expansion of these placeholders by graphs yields the actual transformation rules to be applied. Even rather complex transformations occurring in real-life applications, such as the Pull-Up-Method refactoring operation, can be specified by a single generic rule.

Language Theoretic and Algorithmic Properties ofd-dimensional Collages and Patterns in a Grid

Language theoretic aspects and algorithmic properties of particular classes of context-free collage languages and of patterns generated by iterated function systems are studied. These classes are defined by restricting the allowed transformations to a sort of similarity transformations called grid transformations. It turns out that, thanks to this restriction, the language classes have nice closure properties, and non-trivial questions concerning the generated pictures can be decided.

Adaptive star grammars and their languages

Motivated by applications that require mechanisms for describing the structure of object-oriented programs, adaptive star grammars are introduced, and their fundamental properties are studied. In adaptive star grammars, rules are actually schemata which, via the cloning of so-called multiple nodes, may adapt to potentially infinitely many contexts when they are applied. This mechanism makes adaptive star grammars more powerful than context-free graph grammars. Nevertheless, they turn out to be restricted enough to share some of the basic characteristics of context-free devices. In particular, the underlying substitution operator enjoys associativity and confluence properties quite similar to those of context-free graph grammars, and the membership problem for adaptive star grammars is decidable.

Generating self-affine fractals by collage grammars

Abstract Self-affinity and self-similarity are fundamental concepts in fractal geometry. In this paper, they are related to collage grammars — syntactic devices based on hyperedge replacement that generate sets of collages. Essentially, a collage is a picture consisting of geometric parts like line segments, circles, polygons, polyhedra, etc. The overlay of all collages in a collage language yields a fractal pattern. We show that collage grammars of a special type — so-called increasing generalized Sierpinski grammars — yield self-affine fractals. If one replaces the overlay by an intersection of all generated collages, the same result holds for decreasing generalized Sierpinski grammars. Here, the converse also holds: Every self-affine fractal can be generated by a decreasing generalized Sierpinski grammar, which provides a characterization of this class of fractals.

Tree-based generation of languages of fractals

The notion of P-interpreted top-down tree generators is introduced, combining the nondeterministic nature of grammars as known from formal language theory with the infinite refinement of pictures studied in fractal geometry.

Contextual hyperedge replacement

Contextual hyperedge-replacement grammars (contextual grammars, for short) are an extension of hyperedge replacement grammars. They have recently been proposed as a grammatical method for capturing the structure of object-oriented programs, thus serving as an alternative to the use of meta-models like uml class diagrams in model-driven software design. In this paper, we study the properties of contextual grammars. Even though these grammars are not context-free, one can show that they inherit several of the nice properties of hyperedge replacement grammars. In particular, they possess useful normal forms and their membership problem is in NP.