Adaptive star grammars and their languages

Authors:
Frank Drewes;Berthold Hoffmann;Dirk Janssens;Mark Minas
Affiliations:
Institutionen för datavetenskap, Umeå universitet, S-90187 Umeå, Sweden;Fachbereich Mathematik und Informatik, Universität Bremen, D-28344 Bremen, Germany;Departement Wiskunde-Informatica, Universiteit Antwerpen, B-2020 Antwerpen, Belgium;Fakultät für Informatik, Universität der Bundeswehr München, D-85577 Neubiberg, Germany
Venue:
Theoretical Computer Science
Year:
2010

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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.