On the essence and initiality of conflicts

Understanding conflicts between transformations and rules is an important topic in algebraic graph transformation. A conflict occurs when two transformations are not parallel independent, that is, when after applying one of them the other can no longer occur. We contribute to this research thread by proposing a new characterization of the root causes of conflicts, called “conflict essences”. By exploiting a recently proposed characterization of parallel independence we easily show that the conflict essence of two transformations is empty iff they are parallel independent. Furthermore we show that conflict essences are smaller than the “conflict reasons” previously proposed, and that they uniquely determine the so-called “initial conflicts”. All results hold in categories of Set-valued functors, which include the categories of graphs and typed graphs, and several of them hold in the more general adhesive categories.