Tool-Based Verification of a Relational Vertex Coloring Program

  • Rudolf Berghammer
  • Peter Höfner
  • Insa Stucke
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 9348)


We present different approaches of using a special purpose computer algebra system and theorem provers in software verification. To this end, we first develop a purely algebraic while-program for computing a vertex coloring of an undirected (loop-free) graph. For showing its correctness, we then combine the well-known assertion-based verification method with relation-algebraic calculations. Based on this, we show how automatically to test loop-invariants by means of the RelView tool and also compare the usage of three different theorem provers in respect to the verification of the proof obligations: the automated theorem prover Prover9 and the two proof assistants Coq and Isabelle/HOL. As a result, we illustrate that algebraic abstraction yields verification tasks that can easily be verified with off-the-shelf theorem provers, but also reveal some shortcomings and difficulties with theorem provers that are nowadays available.


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Copyright information

© Springer International Publishing Switzerland 2015

Authors and Affiliations

  • Rudolf Berghammer
    • 1
  • Peter Höfner
    • 2
    • 3
  • Insa Stucke
    • 1
  1. 1.Institut für InformatikChristian-Albrechts-Universität zu KielKielGermany
  2. 2.NICTASydneyAustralia
  3. 3.Computer Science and EngineeringUniversity of New South WalesSydneyAustralia

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