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On the essence and initiality of conflicts in M-adhesive transformation systems
Citation key Azzi2019
Author Guilherme Grochau Azzi and Andrea Corradini and Leila Ribeiro
Year 2019
ISSN 2352-2208
DOI 10.1016/j.jlamp.2019.100482
Journal Journal of Logical and Algebraic Methods in Programming
Volume 109
Publisher Elsevier
Abstract Understanding conflicts between transformation steps and rules is an important topic in algebraic graph transformation. A conflict occurs when two transformation steps are not parallel independent, that is, when after applying one of them the other can no longer occur. A static analysis technique called Critical Pair Analysis allows the detection of all potential conflicts between pairs of rules, by enumerating Critical Pairs. Since these are often too numerous for even simple rules, finding appropriate subsets of critical pairs is the topic of ongoing research. We contribute to this thread by proposing a new characterization for root causes of conflicts, called “conflict essences”, exploiting a recently proposed characterization of parallel independence. Furthermore we show that conflict essences are at least as precise as the “conflict reasons” previously proposed, and uniquely determine the so-called “initial conflicts”, an appropriate subset of critical pairs, under relatively mild assumptions on the underlying category. Finally, we show that several M-adhesive categories of interest have the necessary properties for our results to hold, including typed, attributed and symbolic graphs. While our results are formulated for conflicts, they are directly applicable to dependencies in M-adhesive transformation systems.
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