Annegret Habel

GRAPH GRAMMARS WITH NEGATIVE APPLICATION CONDITIONS

In each graph-grammar approach it is defined how and under which conditions graph productions can be applied to a given graph in order to obtain a derived graph. The conditions under which productions can be applied are called application conditions. Although the generative power of most of the known general graph-grammar approaches is sufficient to generate any recursively enumerable set of graphs, it is often convenient to have specific application conditions for each production. Such application conditions, on the one hand, include context conditions like the existence or non-existence of nodes, edges, or certain subgraphs in the given graph as well as embedding restrictions concerning the morphisms from the left-hand side of the production to the given graph. In this paper, the concept of application conditions introduced by Ehrig and Habel is restricted to contextual conditions, especially negative ones. In addition to the general concept, we state local confluence and the Parallelism Theorem for derivations with application conditions. Finally we study context-free graph grammars with application conditions with respect to their generative power.

Graph transformation for specification and programming

The framework of graph transformation combines the potentials and advantages of both, graphs and rules, to a single computational paradigm. In this paper we present some recent developments in applying graph transformation as a rule-based framework for the specification and development of systems, languages, and tools. After reviewing the basic features of graph transformation, we discuss a selection of applications, including the evaluation of functional expressions, the specification of an interactive graphical tool, an example specification for abstract data types, and the definition of a visual database query language. The case studies indicate the need for suitable structuring principles which are independent of a particular graph transformation approach. To this end, we present the concept of a transformation unit, which allows systematic and structured specification and programming based on graph transformation.

Correctness of high-level transformation systems relative to nested conditions†

In this paper we introduce the notions of nested constraints and application conditions, short nested conditions. For a category associated with a graphical representation such as graphs, conditions are a graphical and intuitive, yet precise, formalism that is well suited to describing structural properties. We show that nested graph conditions are expressively equivalent to first-order graph formulas. A part of the proof includes transformations between two satisfiability notions of conditions, namely -satisfiability and -satisfiability. We consider a number of transformations on conditions that can be composed to construct constraint-guaranteeing and constraint-preserving application conditions, weakest preconditions and strongest postconditions. The restriction of rule applications by conditions can be used to correct transformation systems by pruning transitions leading to states violating given constraints. Weakest preconditions and strongest postconditions can be used to verify the correctness of transformation systems with respect to pre-and postconditions.

May we introduce to you: hyperedge replacement

In this kind of tutorial note, we explain how graphs can be rewritten by edge replacement. The formal definitions are accompanied by intuitive descriptions and a series of examples.

Some Structural Aspects of Hypergraph Languages Generated by Hyperedge Replacement

Hyperedge replacement systems are introduced as a device for generating hypergraph languages including graph languages and string languages (where the strings are uniquely represented as certain graphs). Our concept combines a context-free type of rewriting with a comparatively large generative power. The former is indicated, for example, by a pumping lemma, the latter by the examples (among them you find the refinement of Petri nets, the analysis of flow diagrams, the structural description of molecules and some typical non-context-free string languages).

Double-pushout graph transformation revisited

In this paper we investigate and compare four variants of the double-pushout approach to graph transformation. As well as the traditional approach with arbitrary matching and injective right-hand morphisms, we consider three variations by employing injective matching and/or arbitrary right-hand morphisms in rules. We show that injective matching provides additional expressiveness in two respects: for generating graph languages by grammars without non-terminals and for computing graph functions by convergent graph transformation systems. Then we clarify for each of the three variations whether the well-known commutativity, parallelism and concurrency theorems are still valid and { where this is not the case { give modied results. In particular, for the most general approach with injective matching and arbitrary right-hand morphisms, we establish sequential and parallel commutativity by appropriately strengthening sequential and parallel independence.

Amalgamation of graph transformations: a synchronization mechanism

Abstract In the present paper we generalize the well-known Parallelism Theorem for graph derivations to the Amalgamation Theorem. In this theorem the assumption of “parallel independence” is dropped. For each pair of productions together with a relational production (allowing productions to be associated with each other) we construct a single “amalgamated” production. The Amalgamation Theorem states that graph derivations which respect the given associations can be amalgamated to a single derivation via the “amalgamated” production. The amalgamation of graph transformations can be considered as a synchronization mechanism. The amalgamation concept is applied to synchronization of graph manipulations in a simplified railway control system as well as to a graph grammar formalism for distributed systems (GDS).

From Graph Grammars to High Level Replacement Systems

The algebraic approach to graph grammars — well-known in the literature for several types of graphs and structures — is extended to include several new types of replacement systems, especially the replacement of algebraic specifications which were recently introduced for a rule-based approach to modular system design.

Adhesive High-Level Replacement Categories and Systems

Adhesive high-level replacement (HLR) categories and systems are introduced as a new categorical framework for graph transformation in a broad sense, which combines the well-known concept of HLR systems with the new concept of adhesive categories introduced by Lack and Sobocinski.

Graph Grammars with Application Conditions

The algebraic approach of graph grammars is extended by a very general notion of application conditions which can be defined separately for each production. This extended approach is applied to a small library system in order to show the flexibility of this concept for the design of systems in computer science and related areas. In addition to the general concept we study some special cases of graph grammars with application conditions with respect to their generative power. Finally we state some facts how to extend known results in the algebraic theory of graph grammars to the case with application conditions.