Assemblies as Graph Processes

Abstract. This short paper explores the potential of embedding-based graph rewriting as a tool for understanding natural computing, and in particular self-assembly. The basic point of view is that aggregation steps in self-assembly can be adequately described by graph rewriting steps in an embedding-based graph transformation system: the building blocks of an assembly correspond to occurrences of rewriting rules, and hence assemblies correspond to graph processes. However, meaningful algorithms do not consist only of aggregation steps, but also of global steps in which assemblies are modified. A theoretical algorithm is presented in which the two kinds of steps are combined: on the one hand aggregation steps that build assemblies, and on the other hand global steps which act on the assemblies.