A Static Analysis Technique for Graph Transformation Systems

Abstract

In this paper we introduce a static analysis technique for graph transformation systems. We present an algorithm which, given a graph transformation system and a start graph, produces a finite structure consisting of a hypergraph decorated with transitions (Petri graph) which can be seen as an approximation of the Winskel style unfolding of the graph transformation system. The fact that any reachable graph has an homomorphic image in the Petri graph and the additional causal information provided by transitions allow us to prove several interesting properties of the original system. As an application of the proposed technique we show how it can be used to verify the absence of deadlocks in an infinite-state Dining Philosophers system

Verification of Graph Transformation Systems with Context-Free Specifications

“…Assume that T is such a system. The approximation of the word language T can be intuitively seen as equivalent to a finite automaton A and a counting constraint C. 1 The approximation L is given by L = L(A) ∩ L(C), i.e., the words of L are those accepted by A and satisfying C. Later such counting constraints will be specified via the reachable markings of a Petri net.…”

“…In this section we sketch the algorithm, introduced in [1], for the construction of a finite approximation of the unfolding of a graph transformation system. Of course there is a straightforward counting abstraction via a Petri net which just counts the number of occurrences of each edge, regardless of structure.…”

“…In recent years there have been several approaches directed specifically at the verification of graph transformation systems, for instance [21,10,24,1,2,4,22]. They usually address the following problem: Given a graph transformation system T generating a set reach(T ) of reachable graphs, and a set F of forbidden graphs, is the intersection reach(T ) ∩ F empty?…”

“…This problem is undecidable even for the case in which the set F contains one single graph, and so all approaches approximate the set reach(T ) in some way. In this paper we further develop the approach of [1,2], which-given T -constructs a Petri net whose reachable markings encode a set L of graphs satisfying L ⊇ reach (…”

Graphical Encoding of a Spatial Logic for the π-Calculus

“…In this paper we present an approach [16] to the verification of spatial formulae [4] for π-calculus specifications, based on a graphical encoding for nominal calculi [15]. Even if a few articles have been already proposed on the verification of graphically described systems (see e.g [1,21,23]), to the best of our knowledge our approach is the only one that deals with specification of spatial properties for processes of nominal calculi, based on a graphical presentation. The approach was introduced in previous works, first describing the graphical encoding of processes in a nominal calculus [15] and then an algorithm to verify properties on such representations [16].…”