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. 1

Abstract. Graph rewrite rules, programmed by sequencing and iteration, suffice to define the computable functions on graphs—in theory. In practice however, the control program may become hard to formulate, hard to understand, and even harder to verify. Therefore, we have extended graph rewrite rules by variables that are instantiated by a kind of hyperedge replacement, before the so instantiated rules are applied to a graph. This way, rules can be defined recursively over the structure of the graphs where they apply, in a fully declarative way. Generic rules with variables and recursive rule instantiation have been implemented in the graph rewrite tool GrGen. 1

Abstract. The precise specification of software models is a major concern in model-driven design of object-oriented software. In this paper, we investigate how program graphs, a language-independent model of object-oriented programs, can be specified precisely, with a focus on static structure rather than behavior. Graph grammars are a natural candidate for specifying the structure of a class of graphs. However, neither star grammars—which are equivalent to the well-known hyperedge replacement grammars—nor the recently proposed adaptive star grammars allow all relevant properties of program graphs to be specified. So we extend adaptive star rules by positive and negative application conditions, and show that the resulting conditional adaptive star grammars are powerful enough to generate program graphs. 1