A Modal-Logic Based Graph Abstraction

Authors:
Jörg Bauer;Iovka Boneva;Marcos E. Kurbán;Arend Rensink
Affiliations:
Formal Methods and Tools Group, EWI-INF, University of Twente, Enschede, The Netherlands 7500 AE;Institut für Informatik, Technical University of Munich, Garching bei München, Germany 85748;Former member of Formal Methods and Tools Group, EWI-INF, University of Twente,;Institut für Informatik, Technical University of Munich, Garching bei München, Germany 85748
Venue:
ICGT '08 Proceedings of the 4th international conference on Graph Transformations
Year:
2008

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Abstract

Infinite or very large state spaces often prohibit the successful verification of graph transformation systems. Abstract graph transformation is an approach that tackles this problem by abstracting graphs to abstract graphs of bounded size and by lifting application of productions to abstract graphs. In this work, we present a new framework of abstractions unifying and generalising existing takes on abstract graph transformation. The precision of the abstraction can be adjusted according to the properties to be verified facilitating abstraction refinement. We present a modal logic defined on graphs, which is preserved andreflected by our abstractions. Finally, we demonstrate the usability of the framework by verifying a graph transformation model of a firewall.