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International Conference on Tools and Algorithms for the Construction and Analysis of Systems

TACAS 2021: Tools and Algorithms for the Construction and Analysis of Systems pp 223–241Cite as

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cake_lpr: Verified Propagation Redundancy Checking in CakeML

cake_lpr: Verified Propagation Redundancy Checking in CakeML

  • Yong Kiam Tan  ORCID: orcid.org/0000-0001-7033-246310,
  • Marijn J. H. Heule  ORCID: orcid.org/0000-0002-5587-880110 &
  • Magnus O. Myreen  ORCID: orcid.org/0000-0002-9504-410711 
  • Conference paper
  • Open Access
  • First Online: 23 March 2021

  • 2300 Accesses

  • 6 Citations

Part of the Lecture Notes in Computer Science book series (LNTCS,volume 12652)

Abstract

Modern SAT solvers can emit independently checkable proof certificates to validate their results. The state-of-the-art proof system that allows for compact proof certificates is propagation redundancy (PR). However, the only existing method to validate proofs in this system with a formally verified tool requires a transformation to a weaker proof system, which can result in a significant blowup in the size of the proof and increased proof validation time. This paper describes the first approach to formally verify PR proofs on a succinct representation; we present (i) a new Linear PR (LPR) proof format, (ii) a tool to efficiently convert PR proofs into LPR format, and (iii) cake_lpr, a verified LPR proof checker developed in CakeML. The LPR format is backwards compatible with the existing LRAT format, but extends the latter with support for the addition of PR clauses. Moreover, cake_lpr is verified using CakeML ’s binary code extraction toolchain, which yields correctness guarantees for its machine code (binary) implementation. This further distinguishes our clausal proof checker from existing ones because unverified extraction and compilation tools are removed from its trusted computing base. We experimentally show that LPR provides efficiency gains over existing proof formats and that the strong correctness guarantees are obtained without significant sacrifice in the performance of the verified executable.

Keywords

  • linear propagation redundancy
  • binary code extraction

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Authors and Affiliations

  1. Computer Science Department, Carnegie Mellon University, Pittsburgh, USA

    Yong Kiam Tan & Marijn J. H. Heule

  2. Chalmers University of Technology, Gothenburg, Sweden

    Magnus O. Myreen

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  1. Yong Kiam Tan
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Correspondence to Yong Kiam Tan .

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Editors and Affiliations

  1. Eindhoven University of Technology, Eindhoven, The Netherlands

    Prof. Jan Friso Groote

  2. Aalborg University, Aalborg East, Denmark

    Prof. Kim Guldstrand Larsen

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Tan, Y.K., Heule, M.J.H., Myreen, M.O. (2021). cake_lpr: Verified Propagation Redundancy Checking in CakeML. In: Groote, J.F., Larsen, K.G. (eds) Tools and Algorithms for the Construction and Analysis of Systems. TACAS 2021. Lecture Notes in Computer Science(), vol 12652. Springer, Cham. https://doi.org/10.1007/978-3-030-72013-1_12

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  • DOI: https://doi.org/10.1007/978-3-030-72013-1_12

  • Published: 23 March 2021

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