Resilience of Well-structured Graph Transformation Systems

Abstract

Resilience is a concept of rising interest in computer science and software engineering. For systems in which correctness w.r.t. a safety condition is unachievable, fast recovery is demanded. We investigate resilience problems of graph transformation systems. Our main contribution is the decidability of two resilience problems for well-structured graph transformation systems (with strong compatibility). We prove our results in the abstract framework of well-structured transition systems and apply them to graph transformation systems, incorporating also the concept of adverse conditions. * Supported by the German Research Foundation (DFG) through the Research Training Group (DFG GRK 1765) SCAREWe consider graph constraints [15,9] whose validities are inherited to bigger/smaller graphs.Definition 2 (positive & negative basic graph constraints). The class of positive (basic graph) constraints is defined inductively: (i) ∃G is a positive constraint where G is a graph, (ii) for positive constraints c, c ′ , also c ∨ c ′ , c ∧ c ′ are positive constraints. Analogously, the negative (basic graph) constraints are defined by: (i) ¬∃G is a negative constraint for any graph G, (ii) for negative constraints c, c ′ , also c ∨ c ′ , c ∧ c ′ are negative constraints. A graph G satisfies ∃G ′ if there exists an total injective morphism G ′ ֒→ G. The semantics of the logical operators are as usual. We write G |= c if G satisfies the positive/negative constraint c.