Verifying a Behavioural Logic for Graph Transformation Systems

Paolo Baldan, Andrea Corradini, Barbara König, Bernhard König
2004 Electronical Notes in Theoretical Computer Science  
We propose a framework for the verification of behavioural properties of systems modelled as graph transformation systems. The properties can be expressed in a temporal logic which is basically a µ-calculus where the state predicates are formulae of a monadic second order logic, describing graph properties. The verification technique relies on an algorithm for the construction of finite over-approximations of the unfolding of a graph transformation system. Approximating the Behaviour of GTSs. A
more » ... basic ingredient for the verification of µL2 is a technique, proposed in [5, 6] , for approximating the behaviour of GTSs by means of finite Petri net-like structures, in the spirit of abstract interpretation of reactive systems [22] . More precisely, an approximated unfolding construction maps any given GTS G to finite structures, called coverings of G, which provide "effective" (over-)approximations of the behaviour of G. The accuracy of the approximation can be chosen by the user and arbitrarily increased. Essentially one can require the approximation to be exact up to a certain causal depth k, thus obtaining the so-called k-covering C k (G) of G. The coverings are Petri graphs, i.e., structures consisting of a Petri net with a graphical structure over places. Each C k (G) over-approximates the behaviour of G in the sense that every computation of G is mapped to a
doi:10.1016/j.entcs.2004.08.018 fatcat:q25djbt4ozfpjgj4ac7svx3zwa