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Verification of Galois field based circuits by formal reasoning based on computational algebraic geometry

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Abstract

Algebraic error correcting codes (ECC) are widely used to implement reliability features in modern servers and systems and pose a formidable verification challenge. We present a novel methodology and techniques for provably correct design of ECC logics. The methodology is comprised of a design specification method that directly exposes the ECC algorithm’s underlying math to a verification layer, encapsulated in a tool “BLUEVERI”, which establishes the correctness of the design conclusively by using an apparatus of computational algebraic geometry (Buchberger’s algorithm for Gröbner basis construction). We present results from its application to example circuits to demonstrate the effectiveness of the approach. The methodology has been successfully applied to prove correctness of large error correcting circuits on IBM’s POWER systems to protect memory storage and processor to memory communication, as well as a host of smaller error correcting circuits.

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Notes

  1. Very often the uncorrectable error signal is both an internal signal upon which further things depend and also an output by itself.

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Acknowledgments

The authors would like to thank Shmuel Winograd and Geert Janseen of IBM Research for insightful discussions to help shape the solution.

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Authors and Affiliations

  1. IBM T. J. Watson Research Center, Yorktown Heights, NY, 10598, USA

    Alexey Lvov, Luis A. Lastras-Montaño & Barry Trager

  2. IBM Systems and Technology Group, Austin, TX, 78758, USA

    Viresh Paruthi, Robert Shadowen & Ali El-Zein

Authors
  1. Alexey Lvov
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  2. Luis A. Lastras-Montaño
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  3. Barry Trager
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  4. Viresh Paruthi
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  5. Robert Shadowen
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  6. Ali El-Zein
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Correspondence to Alexey Lvov.

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Lvov, A., Lastras-Montaño, L.A., Trager, B. et al. Verification of Galois field based circuits by formal reasoning based on computational algebraic geometry. Form Methods Syst Des 45, 189–212 (2014). https://doi.org/10.1007/s10703-014-0206-z

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  • DOI: https://doi.org/10.1007/s10703-014-0206-z

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