Graph-transformation verification using monadic second-order logic

  • Authors:

  • Kazuhiro Inaba;Soichiro Hidaka;Zhenjiang Hu;Hiroyuki Kato;Keisuke Nakano

  • Affiliations:

  • National Institute of Informatics, Tokyo, Japan;National Institute of Informatics, Tokyo, Japan;National Institute of Informatics, Tokyo, Japan;National Institute of Informatics, Tokyo, Japan;The University of Electro-Communications, Tokyo, Japan

  • Venue:
  • Proceedings of the 13th international ACM SIGPLAN symposium on Principles and practices of declarative programming
  • Year:
  • 2011

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Abstract

This paper presents a new approach to solving the problem of verification of graph transformation, by proposing a new static verification algorithm for the Core UnCAL, the query algebra for graph-structured databases proposed by Bunemann et al. Given a graph transformation annotated with schema information, our algorithm statically verifies that any graph satisfying the input schema is converted by the transformation to a graph satisfying the output schema. We tackle the problem by first reformulating the semantics of UnCAL into monadic second-order logic (MSO). The logic-based foundation allows to express the schema satisfaction of transformations as the validity of MSO formulas over graph structures. Then by exploiting the two established properties of UnCAL called bisimulation-genericity and compactness, we reduce the problem to the validity of MSO over trees, which has a sound and complete decision procedure. The algorithm has been efficiently implemented; all the graph transformations in this paper and the system web page can be verified within several seconds.