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Formal Relationship between Graph Grammars and Petri Nets.

Korff, Martin; Ribeiro, Leila

In: Cuny, J.; Ehrig, H.; Engels, G.; Rozenberg, G.: Lecture Notes in Computer Science, Vol. 1073; Graph Grammars and Their Applications to Computer Science, pages 288-303. Springer-Verlag, 1996.

Abstract: The main aim of this paper is to analyze the similarities and differences between graph grammars and Petri nets. Particularly we compare the high-level versions of nets and grammars, namely AHL nets and attributed graph grammars and the corresponding flattening constructions to PT nets and labeled graph grammars, and show that these flattenings are compatible (syntactically and semantically) with the translations of nets to grammars. Thus Petri nets are equivalent to their graph grammar translations. Due to the fact that graphs correspond to sets of tokens, Petri nets can syntactically be considered as special (simple) graph grammars. In their basic semantics however this is not precisely true: tokens without individuality are in contrast to corresponding vertices showing individuality. (Reachability and derivation) Trees have been chosen as a common semantical domain.


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