Graph Transformation Model of a Triangulated Network of Mobile Units

A triangulated network of mobile units is modelled by means of a graph trans-formation system in which graph nodes are labelled with geometric coordinates and edges are labelled with distances. Nodes represent mobile units and edges represent wireless radio communication links between them. Under concurrency the model can describe interesting practical scenarios, for example swarms of taxis in an urban environment. The contribution features the enhancement of a graph transformation system by trigonometric calculations. By the way it is also shown that the classical negative edge condition has only limited applicability if a strict locality principle is assumed, and "vice versa" that there are reasonable modeling cases in which this locality principle itself fails to suffice

Logic Based Programmed Structure Rewriting Systems

. This paper presents a new logic based framework for the formal treatment of graph rewriting systems as special cases of programmed rewriting systems for arbitrary relational data structures. Considering its expressive power, the new formalism surpasses almost all variants of nonparallel algebraic as well as algorithmic graph grammar approaches by offering set-oriented pattern matching facilities as well as nonmonotonic reasoning capabilities for checking pre- and postconditions of rewrite rules. Furthermore, the formalism closes the gap between the operation-oriented manipulation of data structures by means of rewrite rules and the declaration-oriented description of data structures by means of logic based languages. Finally, the formalism even offers recursively defined (sub-)programs, by means of which the application of rewrite rules may be regulated. A denotational semantics definition for these (sub-)programs relies on a special variant of fixpoint theory for noncontinuous but m..