A framework for the verification of infinite-state graph transformation systems

  • Authors:

  • Paolo Baldan;Andrea Corradini;Barbara König

  • Affiliations:

  • Dipartimento di Matematica Pura e Applicata, Università di Padova, Italy;Dipartimento di Informatica, Università di Pisa, Italy;Abt. für Informatik und Ang. Kognitionswissenschaft, Universität Duisburg-Essen, Germany

  • Venue:
  • Information and Computation
  • Year:
  • 2008

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Abstract

We propose a technique for the analysis of infinite-state graph transformation systems, based on the construction of finite structures approximating their behaviour. Following a classical approach, one can construct a chain of finite under-approximations (k-truncations) of the Winskel style unfolding of a graph grammar. More interestingly, also a chain of finite over-approximations (k-coverings) of the unfolding can be constructed. The fact that k-truncations and k-coverings approximate the unfolding with arbitrary accuracy is formalised by showing that both chains converge (in a categorical sense) to the full unfolding. We discuss how the finite over- and under-approximations can be used to check properties of systems modelled by graph transformation systems, illustrating this with some small examples. We also describe the Augur tool, which provides a partial implementation of the proposed constructions, and has been used for the verification of larger case studies.