Towards the specification and verification of modal properties for structured systems

System specification formalisms should come with suitable property specification languages and effective verification tools. We sketch a framework for the verification of quantified temporal properties of systems with dynamically evolving structure. We consider visual specification formalisms like graph transformation systems (GTS) where program states are modelled as graphs, and the program behavior is specified by graph transformation rules. The state space of a GTS can be represented as a graph transition system (GTrS), i.e. a transition system with states and transitions labelled, respectively, with a graph, and with a partial morphism representing the evolution of state components. Unfortunately, GTrSs are prohibitively large or infinite even for simple systems, making verification intractable and hence calling for appropriate abstraction techniques

Verification of Random Graph Transformation Systems

AbstractIn this paper we describe some statistical results obtained by the verification of random graph transformation systems (GTSs). As a verification technique we use over-approximation of GTSs by Petri nets. Properties we want to verify are given by markings of Petri nets. We also use counterexample-guided abstraction refinement approach to refine the obtained approximation. A software tool (Augur) supports the verification procedure. The idea of the paper is to see how many of the generated systems can be successfully verified using this technique

Unfolding Shape Graphs

Shape graphs have been introduced in [Ren04a, Ren04b] as an abstraction to be used in model checking object oriented software, where states of the system are represented as graphs. Intuitively, the graphs modeling the states represent the structure of objects dynamically allocated in the heap. State transitions are then generated by applying graph transformation rules corresponding to the statements of the program. Since the state space of such systems is potentially unbounded, the graphs representing the states are abstracted by shape graphs. Graph transformation systems may be analyzed [BCK01, BK02] by constructing finite structures that approximate their behaviour with arbitrary accuracy, by using techniques developed in the context of Petri nets. The approach of [BK02] is to construct a chain of finite under-approximations of the Winskel’s style unfolding of a graph grammar, as well as a chain of finite over-approximations of the unfolding, where both chains converge to the full unfolding. The approximations may then be used to check properties of the underlying graph transformation system. We apply this technique to approximate the behaviour of systems represented by shape graphs and graph tranformation rules

verifying a behavioural logic for graph transformation systems

We propose a framework for the verication of behavioural properties of systems modelled as graph transformation systems. The properties can be expressed in a temporal logic which is basically a -calculus where the state predicates are formulae of a monadic second order logic, describing graph properties. The verication technique relies on an algorithm for the construction of nite over-approximations of the unfolding of a graph transformation system

Towards Guided Trajectory Exploration of Graph Transformation Systems

Graph transformation systems (GTS) are often used for modeling the behavior of complex systems. A common GTS analysis scenario is the exploration of its state space from an initial state to a state adhering to given goals through a proper trajectory. Guided trajectory exploration uses information from some more abstract analysis of the system as hints to reduce the traversed state space. These hints are used to order possible further transitions from a given state (selection) and detect violations early (cut-off), thus pruning unpromising trajectories from the state space. In the current paper, we define cut-off and selection criteria for guiding the trajectory exploration, and use Petri Net analysis results and the dependency relations between rules as hints in our criteria calculation algorithm. The criteria definitions include navigation along dependency relations, various types of ordering for selection and quantifiers for cut-off criteria. Our approach is exemplified on a cloud infrastructure configuration problem

A case study : verifying a mutual exclusion protocol with process creation using graph transformation systems

We verify a mutual exclusion protocol with dynamic process creation based on token passing. The protocol is specified using object-based graph grammars. We introduce the protocol and show how the mutual exclusion property and other properties can be verified using the tool Augur, a verification tool for graph transformation systems based on an approximated unfolding technique

Counterexample-guided abstraction refinement for the analysis of graph transformation systems

Graph transformation systems are a general specification language for systems with dynamically changing topologies, such as mobile and distributed systems. Although in the last few years several analysis and verification methods have been proposed for graph transformation systems, counterexample-guided abstraction refinement has not yet been studied in this setting. We propose a counterexample-guided abstraction refinement technique which is based on the over-approximation of graph transformation systems by Petri nets. We show that a spurious counterexample is caused by merging nodes during the approximation. We present a technique for identifying these merged nodes and splitting them using abstraction refinement, which removes the spurious run. The technique has been implemented in the Augur tool and experimental results are discussed

Approximating the behaviour of graph transformation systems

We propose a technique for the analysis of graph transformation systems based on the construction of finite structures approximating the behaviour of such systems with arbitrary accuracy. Following a classical approach, one can construct a chain of finite under-approximations (k-truncations) of the Winskel’s style unfolding of a graph grammar. More interestingly, also a chain of finite over-approximations (k-coverings) of the unfolding can be constructed and both chains converge (in a categorical sense) to the full unfolding. The finite over- and under-approximations can be used to check properties of a graph transformation system, like safety and liveness properties, expressed in (meaningful fragments of) the modal µ-calculus. This is interpretation