Graph grammars

Schneider, Hans; Erlangen,

doi:10.1007/3-540-08442-8_99

Cited by 2 publications

(1 citation statement)

References 22 publications

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“…They differ mainly in the definition of the embedding transformation. The classification given in [28] distinguishes between algorithmic and algebraic graph rewriting systems. A survey on both directions is given in [19], for an introduction to the algebraic approach see [8].…”

Section: Introductionmentioning

confidence: 99%

On the generative power of sequential and parallel programmed graph grammars

Bunke

1982

Computing

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--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].

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Section: Introductionmentioning

confidence: 99%

On the generative power of sequential and parallel programmed graph grammars

Bunke

1982

Computing

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A tutorial and bibliographical survey on graph grammars

Nagl

Graph-Grammars and Their Application to Computer Science and Biology

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In the first section we make some remarks(witout going into any details) about the main application fields of graph grammars to motivate their investigation. In section 2 and 3 we give a short and informal overview on most of the approaches for sequential and parallel graph grammars known in literature. In the last part we introduce some of the modifications and extensions enforced by several applications and give some comments on implementation of graph grammars realized so far. i, APPLICATIONS OF GRAPH GRAMMARSPicture and graph grammars have been introduced first for picture processing problems e.g. for the recognition of chromosomes, handprinted letters, bubble and fog chamber pictures of elementary particle physics (see part PA of the bibliography for references corresponding to "grammatical" or "linguistic" pattern recognition).In these fields there is no alternative to automatic picture processing. For bubble and fog chamber pictures we have no finite number of picture classes such that any picture can be related to one of these classes. Any point of a picture can be the origin of a subpicture if a disintegration takes place there. On the other hand it is possible to state recursive rules saying how subpictures are generated and how they are connected. Thus, for any class of such pictures one can give a finite set of rules, i.e. a picture grammar. A part of the picture processing problem is reduced to the problem of syntax analysis of the description of the picture bymeans of a picture grammar. The advantage of this method is that in the case of success of the syntax analysis one has not only a yes-no-decision but a description of the structure of the considered picture. A picture can be described by listing its subpictures and the geometric relations between them as "is right of", "is below of", "lies within", "is connected with" etc.If we introduce for any occurrence of a subpicture a node which is labelled with the subpicture itself and if two nodes are connected by an edge, the label of which expresses a geometric relation iff the corresponding subpictures satisfy this relation,

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Graph grammars

Cited by 2 publications

References 22 publications

On the generative power of sequential and parallel programmed graph grammars

On the generative power of sequential and parallel programmed graph grammars

A tutorial and bibliographical survey on graph grammars

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