{"title":"用直接映射求解布尔可满足性的具有三体自旋相互作用的可重构CMOS Ising机","authors":"Yuqi Su;Tony Tae-Hyoung Kim;Bongjin Kim","doi":"10.1109/LSSC.2023.3303332","DOIUrl":null,"url":null,"abstract":"Ising machines have recently emerged as efficient computers for nondeterministic polynomial-time hard (NP-hard) combinatorial optimization problems (COPs). While most prior works have built their Ising machines with spins arranged in a graph with only two-body interactions, many real-world COPs, including a popular Boolean satisfiability (SAT) problem, often involve many-body spin interactions. This letter presents a novel Ising machine that can directly map and solve 3-SAT problems (i.e., SAT problems with at most three literals per clause). The proposed Ising machine eliminates the hardware overhead due to the ancillary spins required for approximate mapping used for the prior Ising machines with two-body interactions only. For evaluation, a prototype chip is fabricated using 65 nm and solved 3-SAT problems and their variants (a weighted max 3-SAT). The 65-nm chip occupies 0.345 mm 2 for 128–1024 embedded spins with 8-bit interaction coefficients and consumes \n<inline-formula> <tex-math>$3.73~\\mu \\text{W}$ </tex-math></inline-formula>\n per spin at 1.2 V and 64 MHz.","PeriodicalId":13032,"journal":{"name":"IEEE Solid-State Circuits Letters","volume":null,"pages":null},"PeriodicalIF":2.2000,"publicationDate":"2023-08-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"1","resultStr":"{\"title\":\"A Reconfigurable CMOS Ising Machine With Three-Body Spin Interactions for Solving Boolean Satisfiability With Direct Mapping\",\"authors\":\"Yuqi Su;Tony Tae-Hyoung Kim;Bongjin Kim\",\"doi\":\"10.1109/LSSC.2023.3303332\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"Ising machines have recently emerged as efficient computers for nondeterministic polynomial-time hard (NP-hard) combinatorial optimization problems (COPs). While most prior works have built their Ising machines with spins arranged in a graph with only two-body interactions, many real-world COPs, including a popular Boolean satisfiability (SAT) problem, often involve many-body spin interactions. This letter presents a novel Ising machine that can directly map and solve 3-SAT problems (i.e., SAT problems with at most three literals per clause). The proposed Ising machine eliminates the hardware overhead due to the ancillary spins required for approximate mapping used for the prior Ising machines with two-body interactions only. For evaluation, a prototype chip is fabricated using 65 nm and solved 3-SAT problems and their variants (a weighted max 3-SAT). The 65-nm chip occupies 0.345 mm 2 for 128–1024 embedded spins with 8-bit interaction coefficients and consumes \\n<inline-formula> <tex-math>$3.73~\\\\mu \\\\text{W}$ </tex-math></inline-formula>\\n per spin at 1.2 V and 64 MHz.\",\"PeriodicalId\":13032,\"journal\":{\"name\":\"IEEE Solid-State Circuits Letters\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":2.2000,\"publicationDate\":\"2023-08-08\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"1\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"IEEE Solid-State Circuits Letters\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://ieeexplore.ieee.org/document/10210653/\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q3\",\"JCRName\":\"COMPUTER SCIENCE, HARDWARE & ARCHITECTURE\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"IEEE Solid-State Circuits Letters","FirstCategoryId":"1085","ListUrlMain":"https://ieeexplore.ieee.org/document/10210653/","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"COMPUTER SCIENCE, HARDWARE & ARCHITECTURE","Score":null,"Total":0}
引用次数: 1
摘要
伊辛机最近成为解决不确定多项式时间困难(NP-困难)组合优化问题(COP)的有效计算机。虽然大多数先前的工作都构建了Ising机器,其自旋排列在只有两个身体相互作用的图中,但许多现实世界的COP,包括一个流行的布尔可满足性(SAT)问题,通常涉及许多身体-自旋相互作用。这封信提出了一种新颖的Ising机器,它可以直接映射和解决3-SAT问题(即每个子句最多有三个文字的SAT问题)。所提出的Ising机器消除了由于用于仅具有两个身体相互作用的现有Ising机器的近似映射所需的辅助自旋而引起的硬件开销。为了进行评估,使用65nm制造了原型芯片,并解决了3-SAT问题及其变体(加权最大3-SAT)。对于128–1024个具有8位相互作用系数的嵌入自旋,65 nm芯片占用0.345 mm 2,并且在1.2 V和64 MHz下每自旋消耗3.73美元。
A Reconfigurable CMOS Ising Machine With Three-Body Spin Interactions for Solving Boolean Satisfiability With Direct Mapping
Ising machines have recently emerged as efficient computers for nondeterministic polynomial-time hard (NP-hard) combinatorial optimization problems (COPs). While most prior works have built their Ising machines with spins arranged in a graph with only two-body interactions, many real-world COPs, including a popular Boolean satisfiability (SAT) problem, often involve many-body spin interactions. This letter presents a novel Ising machine that can directly map and solve 3-SAT problems (i.e., SAT problems with at most three literals per clause). The proposed Ising machine eliminates the hardware overhead due to the ancillary spins required for approximate mapping used for the prior Ising machines with two-body interactions only. For evaluation, a prototype chip is fabricated using 65 nm and solved 3-SAT problems and their variants (a weighted max 3-SAT). The 65-nm chip occupies 0.345 mm 2 for 128–1024 embedded spins with 8-bit interaction coefficients and consumes
$3.73~\mu \text{W}$
per spin at 1.2 V and 64 MHz.