Formal Verification of Invariants for Attributed Graph Transformation Systems Based on Nested Attributed Graph Conditions

Abstract

The behavior of various kinds of dynamic systems can be formalized using typed attributed graph transformation systems (GTSs). The states of these systems are then modelled using graphs and the evolution of the system from one state to another is described by a finite set of graph transformation rules. GTSs with small finite state spaces can be analyzed with ease but analysis is intractable/undecidable for GTSs inducing large/infinite state spaces due to the inherent expressiveness of GTSs. Hence, automatic analysis procedures do not terminate or return indefinite or incorrect results. We propose an analysis procedure for establishing state-invariants for GTSs that are given by nested graph conditions (GCs). To this end, we formalize a symbolic analysis algorithm based on k-induction using Isabelle, apply it to GTSs and GCs over typed attributed graphs, develop support to single out some spurious counterexamples, and demonstrate the feasibility of the approach using our prototypical implementation.