非线性整数算法的验证

Journal of the ACM (JACM) Pub Date : 2019-06-14 DOI:10.1145/3319396

P. Beame, Vincent Liew

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引用次数: 7

摘要

我们通过展示如何为最广泛使用的乘法器电路的许多性质构造短分辨率证明，消除了使用CDCL SAT求解器有效验证非线性整数算法的关键障碍。这样简短的证明被认为是不存在的。更准确地说，我们给出了数组、对角线和Booth乘法器上任意2度恒等式的nO(1)大小正则分辨率证明，以及Wallace树乘法器上这些恒等式的nO(log n)大小证明。

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Toward Verifying Nonlinear Integer Arithmetic

We eliminate a key roadblock to efficient verification of nonlinear integer arithmetic using CDCL SAT solvers, by showing how to construct short resolution proofs for many properties of the most widely used multiplier circuits. Such short proofs were conjectured not to exist. More precisely, we give nO(1) size regular resolution proofs for arbitrary degree 2 identities on array, diagonal, and Booth multipliers and nO(log n) size proofs for these identities on Wallace tree multipliers.

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Journal of the ACM (JACM)

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