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Tool-Based Verification of a Relational Vertex Coloring Program

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Book cover Relational and Algebraic Methods in Computer Science (RAMICS 2015)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 9348))

Abstract

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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Author information

Authors and Affiliations

  1. Institut für Informatik, Christian-Albrechts-Universität zu Kiel, Kiel, Germany

    Rudolf Berghammer & Insa Stucke

  2. NICTA, Sydney, Australia

    Peter Höfner

  3. Computer Science and Engineering, University of New South Wales, Sydney, Australia

    Peter Höfner

Authors
  1. Rudolf Berghammer
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  2. Peter Höfner
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  3. Insa Stucke
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Editor information

Editors and Affiliations

  1. McMaster University, Hamilton, Ontario, Canada

    Wolfram Kahl

  2. Brock University, St. Catharines, Ontario, Canada

    Michael Winter

  3. Universidade do Minho, Braga, Portugal

    José Oliveira

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Berghammer, R., Höfner, P., Stucke, I. (2015). Tool-Based Verification of a Relational Vertex Coloring Program. In: Kahl, W., Winter, M., Oliveira, J. (eds) Relational and Algebraic Methods in Computer Science. RAMICS 2015. Lecture Notes in Computer Science(), vol 9348. Springer, Cham. https://doi.org/10.1007/978-3-319-24704-5_17

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  • DOI: https://doi.org/10.1007/978-3-319-24704-5_17

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-24703-8

  • Online ISBN: 978-3-319-24704-5

  • eBook Packages: Computer ScienceComputer Science (R0)

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