On the generative power of sequential and parallel programmed graph grammars

Abstract

--ZusammenfassungOn the Generative Power of Sequential and Parallel Programmed Graph Grammars. Programmed graph grammars are formally introduced and their generative power is investigated. Programmed graph grammars differ from other approaches to graph grammars in the so-called control diagram which controls the application order of productions. Restricting the form of the productions of a programmed graph grammar we get several classes of graph languages. These are compared mutually as well as with the hierarchy introduced by Nagl [18]. For unrestricted and monotone productions corresponding classes of graph languages coincide, while the class of context free programmed graph languages is properly contained in the class of context free graph languages in the sense of [18]. AMS Subject Classifications: 68F05.Key words." Graph, graph grammars, embedding transformation, sequential replacement, parallel replacement, generative power. Zur generativen M~ichtigkeit yon sequentiellen und parallelen programmierten Graph-Grammatiken.Programmierte Graph-Grammatiken werden formal definiert und bezfiglich ihrer generativen Mfichtigkeit untersucht. Programmierte Graph-Grammatiken unterscheiden sich yon anderen Graph-Grammatik-Ansiitzen durch das sogenannte Kontrolldiagramm, welches die Reihenfolge steuert, in der Produktionen angewendet werden. Durch Einschr/inkung der Gestalt der Produktionen erh~ilt man verschiedene Klassen von Graph-Sprachen. Diese werden untereinander sowie mit der yon Nagl [18] eingeffihrten Hierarchic verglichen. Im Falle von uneingeschr/inkten und monotonen Produktionen fallen einander entsprechende Klassen von Graph-Sprachen zusammen, w~ihrend die Klasse der kontextfreien programmierten Graph-Sprachen echt enthalten ist in der Klasse der kontextfreien Graph-Sprachen nach [18].

A survey of graph grammars: theory and applications

“…A programmed grammar no longer relies on the distinction between terminals and non-terminals to control the termination of a derivation. Programmed string grammars were introduced in Wose691; Bunke generalized this to graph grammars in 1974 (see [Bunk82b]). Programming is expressed via a control diagram, which specifies the set of productions to try next, conditional on the successful or failed application of the current production.…”

“…Bunk82a][FaB192], but it does not increase the generative power of the grammar[Bunk82b]. (By contrast, a programmed context-free string grammar can generate a context-sensitive language[Fu82].…”