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Double-pushout graph transformation revisited

  • ANNEGRET HABEL (a1), JÜRGEN MÜLLER (a2) and DETLEF PLUMP (a3)

Abstract

In this paper we investigate and compare four variants of the double-pushout approach to graph transformation. As well as the traditional approach with arbitrary matching and injective right-hand morphisms, we consider three variations by employing injective matching and/or arbitrary right-hand morphisms in rules. We show that injective matching provides additional expressiveness in two respects: for generating graph languages by grammars without non-terminals and for computing graph functions by convergent graph transformation systems. Then we clarify for each of the three variations whether the well-known commutativity, parallelism and concurrency theorems are still valid and – where this is not the case – give modified results. In particular, for the most general approach with injective matching and arbitrary right-hand morphisms, we establish sequential and parallel commutativity by appropriately strengthening sequential and parallel independence.

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This research was partly supported by the ESPRIT Working Group APPLIGRAPH. This paper is an extension of Habel et al. (2000).

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Double-pushout graph transformation revisited

  • ANNEGRET HABEL (a1), JÜRGEN MÜLLER (a2) and DETLEF PLUMP (a3)

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