{"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}
引用次数: 7
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.
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