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

{"title":"非线性整数算法的验证","authors":"P. Beame, Vincent Liew","doi":"10.1145/3319396","DOIUrl":null,"url":null,"abstract":"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.","PeriodicalId":17199,"journal":{"name":"Journal of the ACM (JACM)","volume":"105 1","pages":"1 - 30"},"PeriodicalIF":0.0000,"publicationDate":"2019-06-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"7","resultStr":"{\"title\":\"Toward Verifying Nonlinear Integer Arithmetic\",\"authors\":\"P. Beame, Vincent Liew\",\"doi\":\"10.1145/3319396\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"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.\",\"PeriodicalId\":17199,\"journal\":{\"name\":\"Journal of the ACM (JACM)\",\"volume\":\"105 1\",\"pages\":\"1 - 30\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2019-06-14\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"7\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Journal of the ACM (JACM)\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.1145/3319396\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Journal of the ACM (JACM)","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1145/3319396","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}

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。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

查看原文本刊更多论文

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.

求助全文

通过发布文献求助，成功后即可免费获取论文全文。去求助

来源期刊

Journal of the ACM (JACM)

自引率

0.00%

发文量