Graph Automata and Their Application to the Verification of Dynamic Systems

The aim of this thesis is to provide verification techniques based on formal language theory and graph theory for graph transformation systems. Graph transformation systems can be used in a large number of application areas. In many cases it is very natural to model concurrent and distributed systems or other systems, where evolving graph-like structures play a role, by means of graph transformation systems. However, systems which are modelled by graph-like structures usually have an additional level of complexity compared to rule-based systems where states have either a word or tree structure. But since these latter structures have a well-established theory which can be used for several verification techniques, it is natural to ask for an adaption to the setting of graph-like structures. Especially the regular word and tree languages have been studied with great success. In this work we will study regular graph languages – often called recognizable graph languages – as introduced by Courcelle. For this purpose, we will generalize finite automata and tree automata to obtain automata which accept graphs. But similar to decompositions of words into letters in the case of finite automata, these graphaccepting automata depend on so-called cospan decompositions of graphs. Hence, we investigate the connection between cospan decompositions and the well-known notions of path and tree decompositions. Subsequently, we introduce different notions of graph-accepting automata: the categorial notion of automaton functors presented by Bruggink and König, consistent tree automata as generalization of tree automata (accepting tree-like decompositions of graphs) and graph automata as a more automaton-theoretic view on automaton functors (accepting path-like decompositions of graphs). Due to the acceptance of pathlike decompositions graph automata are of special interest to us, since this automaton model is highly comparable to finite automata. Therefore, many techniques for finite automata can be adapted to the setting of graph automata. Precisely, we study how recent automaton-based techniques solving the language inclusion problem for finite automata can be adapted for graph automata and can be used for invariant checking in graph transformation systems. But since graph automata suffer from a combinatorial explosion in the size of the maximally permitted pathwidth, we develop techniques to symbollically represent graph automata by means of binary decision diagrams. Finally, we introduce the prototype implementation of a tool suite, called Raven, for creating and manipulating graph automata. We use this tool for a number of experiments and discuss the runtime results.