用 SAT 求解器检测等面多面体

arXiv - CS - Discrete Mathematics Pub Date : 2024-06-24 DOI:arxiv-2406.16407

Craig S. KaplanUniversity of Waterloo

{"title":"用 SAT 求解器检测等面多面体","authors":"Craig S. KaplanUniversity of Waterloo","doi":"arxiv-2406.16407","DOIUrl":null,"url":null,"abstract":"I show how to express the question of whether a polyform tiles the plane\nisohedrally as a Boolean formula that can be tested using a SAT solver. This\napproach is adaptable to a wide range of polyforms, requires no special-case\ncode for different isohedral tiling types, and integrates seamlessly with\nexisting software for computing Heesch numbers of polyforms.","PeriodicalId":501216,"journal":{"name":"arXiv - CS - Discrete Mathematics","volume":"39 1","pages":""},"PeriodicalIF":0.0000,"publicationDate":"2024-06-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Detecting Isohedral Polyforms with a SAT Solver\",\"authors\":\"Craig S. KaplanUniversity of Waterloo\",\"doi\":\"arxiv-2406.16407\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"I show how to express the question of whether a polyform tiles the plane\\nisohedrally as a Boolean formula that can be tested using a SAT solver. This\\napproach is adaptable to a wide range of polyforms, requires no special-case\\ncode for different isohedral tiling types, and integrates seamlessly with\\nexisting software for computing Heesch numbers of polyforms.\",\"PeriodicalId\":501216,\"journal\":{\"name\":\"arXiv - CS - Discrete Mathematics\",\"volume\":\"39 1\",\"pages\":\"\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2024-06-24\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"arXiv - CS - Discrete Mathematics\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/arxiv-2406.16407\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"arXiv - CS - Discrete Mathematics","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/arxiv-2406.16407","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}

引用次数: 0

摘要

我展示了如何用布尔公式来表达多面体是否平铺平面的问题，该布尔公式可以使用 SAT 求解器进行测试。这种方法适用于各种多面体，不需要为不同的等面平铺类型编写特殊的案例代码，而且可以与现有的计算多面体海斯数的软件无缝集成。

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

微信好友朋友圈 QQ好友复制链接

本刊更多论文

Detecting Isohedral Polyforms with a SAT Solver

I show how to express the question of whether a polyform tiles the plane isohedrally as a Boolean formula that can be tested using a SAT solver. This approach is adaptable to a wide range of polyforms, requires no special-case code for different isohedral tiling types, and integrates seamlessly with existing software for computing Heesch numbers of polyforms.

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

arXiv - CS - Discrete Mathematics

自引率

0.00%

发文量

期刊最新文献

Reconfiguration of labeled matchings in triangular grid graphs Decision problems on geometric tilings Ants on the highway A sequential solution to the density classification task using an intermediate alphabet Complexity of Deciding the Equality of Matching Numbers