Parametrized verification of linear networks using automata as invariants
In this paper we proposed a formalism based on automata on two dimensional strings for specifying inductive invariants for proving correctness of families of linear and circular networks. We proved our inductive approach to be sound and complete (semantical completeness). We have illustrated our approach by simple examples.
We have also given the inductive approach for verification of parametrized systems under fairness. In this case, we use generalized Buchi automata (or Streett automata) as inductive invariants. For this case, we have proved the soundness theorem.
As part of future work, it will be interesting to automate the different parts of the induction based approach and apply them to real practical examples. It will also be interesting to extend our approach to networks defined by context free grammars [SG89]. Further more, it will also be interesting to investigate logic based approaches for specification of the invariants.
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