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Nullstellensatz-Proofs for Multiplier Verification

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Book cover Computer Algebra in Scientific Computing (CASC 2020)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 12291))

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Abstract

Automated reasoning techniques based on computer algebra are an essential ingredient in formal verification of gate-level multiplier circuits. Generating and independently checking proof certificates helps to validate the verification results. Two algebraic proof systems, Nullstellensatz and polynomial calculus, are well-known in proof complexity. The practical application of the polynomial calculus has been studied recently. However, producing and checking Nullstellensatz certificates for multiplier verification has not been considered so far. In this paper we show how Nullstellensatz proofs can be generated as a by-product of multiplier verification and present our Nullstellensatz proof checker Nuss-Checker. Additionally, we prove quadratic upper bounds on the proof size for simple array multipliers.

This work is supported by the LIT AI Lab funded by the State of Upper Austria.

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Notes

  1. 1.

    http://fmv.jku.at/nussproofs.

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Authors and Affiliations

  1. Johannes Kepler University, Linz, Austria

    Daniela Kaufmann & Armin Biere

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  1. Daniela Kaufmann
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  2. Armin Biere
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Correspondence to Daniela Kaufmann .

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Editors and Affiliations

  1. University of Lille, Villeneuve d’Ascq, France

    François Boulier

  2. Coventry University, Coventry, UK

    Matthew England

  3. Plekhanov Russian University of Economics, Moscow, Russia

    Timur M. Sadykov

  4. Institute of Theoretical and Applied Mechanics, Novosibirsk, Russia

    Evgenii V. Vorozhtsov

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Kaufmann, D., Biere, A. (2020). Nullstellensatz-Proofs for Multiplier Verification. In: Boulier, F., England, M., Sadykov, T.M., Vorozhtsov, E.V. (eds) Computer Algebra in Scientific Computing. CASC 2020. Lecture Notes in Computer Science(), vol 12291. Springer, Cham. https://doi.org/10.1007/978-3-030-60026-6_21

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  • DOI: https://doi.org/10.1007/978-3-030-60026-6_21

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