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Changing Labels in the Double-Pushout Approach Can Be Treated Categorically

by: Hans J. Schneider

In: Formal Methods in Software and Systems Modeling, Vol. 3393Springer (2005) , p. 134--149.

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URL:	http://www.springerlink.com/content/3vhq3rxju0f3ye3j

In the double-pushout approach to graph transformations, most authors assume the left-hand side to be injective, since the noninjective case leads to ambiguous results. Taking into consideration productions that change labels, however, may add ambiguity even in the case of injective graph productions. A well-known solution to this problem is restricting the categorical treatment to the underlying graphs, whereas the labels on the derived graph are defined by other means. In this paper, we resume the detailed results on arbitrary left-hand sides that Ehrig and Kreowski have already given in 1976. We apply these results to the case of relabeling such that we can retain the elegant categorical constructions at the level of labeled graphs. ER -

Description

SpringerLink - Buchkapitel

BibTeX record

@incollection{schneider:05,
  abstract = {In the double-pushout approach to graph transformations, most authors assume the left-hand side to be injective, since the noninjective case leads to ambiguous results. Taking into consideration productions that change labels, however, may add ambiguity even in the case of injective graph productions. A well-known solution to this problem is restricting the categorical treatment to the underlying graphs, whereas the labels on the derived graph are defined by other means. In this paper, we resume the detailed results on arbitrary left-hand sides that Ehrig and Kreowski have already given in 1976. We apply these results to the case of relabeling such that we can retain the elegant categorical constructions at the level of labeled graphs.
ER  -},
  added-at = {2010-03-13T18:06:41.000+0100},
  author = {Schneider, Hans J.},
  biburl = {http://www.bibsonomy.org/bibtex/2a5e85dae470a01ca9c93e2e004fe5b55/minas},
  booktitle = {Formal Methods in Software and Systems Modeling},
  crossref = {festschrift-ehrig:05},
  description = {SpringerLink - Buchkapitel},
  editor = {Kreowski, Hans-Jörg and Montanari, Ugo and Orejas, Fernando and Rozenberg, Grzegorz and Taentzer, Gabriele},
  interhash = {f83b719567357f2490ac23f2a4d2fa5b},
  intrahash = {a5e85dae470a01ca9c93e2e004fe5b55},
  keywords = {2005 GraTra},
  pages = {134--149},
  publisher = {Springer},
  series = {Lecture Notes in Computer Science},
  timestamp = {2010-03-13T18:06:41.000+0100},
  title = {Changing Labels in the Double-Pushout Approach Can Be Treated Categorically},
  url = {http://www.springerlink.com/content/3vhq3rxju0f3ye3j},
  volume = 3393,
  year = 2005
}

Endnote record

%0 Book Section
%1 schneider:05
%A Schneider, Hans J.
%B Formal Methods in Software and Systems Modeling
%D 2005
%E Kreowski, Hans-Jörg
%E Montanari, Ugo
%E Orejas, Fernando
%E Rozenberg, Grzegorz
%E Taentzer, Gabriele
%I Springer
%K 
%P 134--149
%T Changing Labels in the Double-Pushout Approach Can Be Treated Categorically
%U http://www.springerlink.com/content/3vhq3rxju0f3ye3j
%V 3393
%X In the double-pushout approach to graph transformations, most authors assume the left-hand side to be injective, since the noninjective case leads to ambiguous results. Taking into consideration productions that change labels, however, may add ambiguity even in the case of injective graph productions. A well-known solution to this problem is restricting the categorical treatment to the underlying graphs, whereas the labels on the derived graph are defined by other means. In this paper, we resume the detailed results on arbitrary left-hand sides that Ehrig and Kreowski have already given in 1976. We apply these results to the case of relabeling such that we can retain the elegant categorical constructions at the level of labeled graphs.
ER  -