A framework for the verification of infinite-state graph transformation systems

Abstract

We propose a technique for the analysis of infinite-state graph transformation systems, based on the construction of finite structures approximating their behaviour. Following a classical approach, one can construct a chain of finite under-approximations ( k-truncations) of the Winskel style unfolding of a graph grammar. More interestingly, also a chain of finite over-approximations ( k-coverings) of the unfolding can be constructed. The fact that k-truncations and k-coverings approximate the unfolding with arbitrary accuracy is formalised by showing that both chains converge (in a categorical sense) to the full unfolding. We discuss how the finite over- and under-approximations can be used to check properties of systems modelled by graph transformation systems, illustrating this with some small examples. We also describe the Augur tool, which provides a partial implementation of the proposed constructions, and has been used for the verification of larger case studies.