Adaptive star grammars and their languages

Abstract

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.

Contextual hyperedge replacement

“…Inclusion of languages studied in this paper and in [3,13] tions [11]. Furthermore, we aim at an improved parsing algorithm for contextual grammars that are unambiguous modulo associativity and commutativity of certain replicative rules.…”

“…The authors have been working on several extensions of hyperedge replacement. Adaptive star replacement [3], devised with D. Janssens and N. Van Eetvelde, allows variables to be attached to arbitrary, unordered sets of nodes. Their generative power is sufficient for defining sophisticated software models like program graphs [6].…”

Adaptive Star Grammars for Graph Models

“…Both formalisms can specify context-free compositions of graphs in the sense of [3], but fail to define simple languages such as the language of all graphs. Adaptive star grammars [4] overcome these limitations by means of a cloning mechanism that makes its rules more powerful.…”

“…The second rule adds edges between border nodes, and the third removes the nonterminal node. A more conventional way to draw the second rule can be obtained by "unfolding" it in two steps, like this: Let us briefly discuss the two main differences between the definition of adaptive star grammars used here and the one in [4]. Firstly, using the terminology of [4], we have restricted ourselves to early cloning, i.e., cloning produces only singular nodes.…”

“…Program graphs have a particular structure: They are composed in a nested fashion according to a context-free syntax, and contain references from entities to their declarations that respect specific scope rules. We define program graphs by adaptive star grammars [4], an extension of the well-known hyperedge and node replacement grammars [11]. We further extend these grammars to enhance the definition and understanding of rules.…”