Abstract
We investigate and compare four variants of the double-pushout approach to graph transformation. Besides 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. For each of the three variations, we clarify whether the well-known commutativity 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. We also show that injective matching provides additional expressiveness in two respects, viz. for generating graph languages by grammars without nonterminals and for computing graph functions by convergent graph transformation systems.
This research was partly supported by the ESPRITWorking Group APPLIGRAPH. Research of the second author was also supported by the EC TMR Network GETGRATS, through the Universities of Antwerp and Pisa. Part of the work of the third author was done while he was visiting the Vrije Universiteit in Amsterdam.
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Habel, A., Müller, J., Plump, D. (2000). Double-Pushout Approach with Injective Matching. In: Ehrig, H., Engels, G., Kreowski, HJ., Rozenberg, G. (eds) Theory and Application of Graph Transformations. TAGT 1998. Lecture Notes in Computer Science, vol 1764. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-46464-8_8
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DOI: https://doi.org/10.1007/978-3-540-46464-8_8
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