Talk "On the Essence and Initiality of Conflicts"

by Andrea Corradini

Sun, 07 April 2019 at 01:00 pm in Prague, Czech Republic

Joint work with: Guilherme Grochau Azzi and Leila Ribeiro

Abstract: 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. 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 of the root causes of conflicts, called ``conflict essences'', exploiting a recently proposed characterization of parallel independence. Furthermore we show that conflict essences are smaller than the ``conflict reasons'' previously proposed, and that they uniquely determine the so-called ``initial conflicts'', an appropriate subset of critical pairs, under relatively mild assumptions of the underlying category. 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.