You can only be lucky once: optimal gossip for epistemic goals

IF 0.4 4区 计算机科学 Q4 COMPUTER SCIENCE, THEORY & METHODS Mathematical Structures in Computer Science Pub Date : 2024-04-19 DOI:10.1017/s0960129524000082
Hans van Ditmarsch, Malvin Gattinger
{"title":"You can only be lucky once: optimal gossip for epistemic goals","authors":"Hans van Ditmarsch, Malvin Gattinger","doi":"10.1017/s0960129524000082","DOIUrl":null,"url":null,"abstract":"It is known that without synchronization via a global clock one cannot obtain common knowledge by communication. Moreover, it is folklore that without communicating higher-level information one cannot obtain arbitrary higher-order shared knowledge. Here, we make this result precise in the setting of gossip where agents make one-to-one telephone calls to share secrets: we prove that “everyone knows that everyone knows that everyone knows all secrets” is unsatisfiable in a logic of knowledge for gossiping. We also prove that, given <jats:italic>n</jats:italic> agents, <jats:inline-formula> <jats:alternatives> <jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" mime-subtype=\"png\" xlink:href=\"S0960129524000082_inline1.png\" /> <jats:tex-math> $2n-3$ </jats:tex-math> </jats:alternatives> </jats:inline-formula> calls are optimal to reach “someone knows that everyone knows all secrets” and that <jats:inline-formula> <jats:alternatives> <jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" mime-subtype=\"png\" xlink:href=\"S0960129524000082_inline2.png\" /> <jats:tex-math> $n - 2 + \\binom{n}{2}$ </jats:tex-math> </jats:alternatives> </jats:inline-formula> calls are optimal to reach “everyone knows that everyone knows all secrets.”","PeriodicalId":49855,"journal":{"name":"Mathematical Structures in Computer Science","volume":null,"pages":null},"PeriodicalIF":0.4000,"publicationDate":"2024-04-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Mathematical Structures in Computer Science","FirstCategoryId":"94","ListUrlMain":"https://doi.org/10.1017/s0960129524000082","RegionNum":4,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q4","JCRName":"COMPUTER SCIENCE, THEORY & METHODS","Score":null,"Total":0}
引用次数: 0

Abstract

It is known that without synchronization via a global clock one cannot obtain common knowledge by communication. Moreover, it is folklore that without communicating higher-level information one cannot obtain arbitrary higher-order shared knowledge. Here, we make this result precise in the setting of gossip where agents make one-to-one telephone calls to share secrets: we prove that “everyone knows that everyone knows that everyone knows all secrets” is unsatisfiable in a logic of knowledge for gossiping. We also prove that, given n agents, $2n-3$ calls are optimal to reach “someone knows that everyone knows all secrets” and that $n - 2 + \binom{n}{2}$ calls are optimal to reach “everyone knows that everyone knows all secrets.”
查看原文
分享 分享
微信好友 朋友圈 QQ好友 复制链接
本刊更多论文
你只能幸运一次:认识论目标的最佳流言
众所周知,没有全局时钟的同步,就无法通过通信获得共同知识。此外,众所周知,如果不交流高层信息,就无法获得任意的高阶共享知识。在这里,我们将这一结果精确地应用于代理人通过一对一通话来分享秘密的闲聊中:我们证明 "每个人都知道每个人都知道每个人都知道所有秘密 "在闲聊的知识逻辑中是不可满足的。我们还证明,给定 n 个代理人,要达到 "有人知道每个人都知道所有秘密",2n-3$ 的通话是最优的;要达到 "每个人都知道每个人都知道所有秘密",$n - 2 + \binom{n}{2}$ 的通话是最优的。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
求助全文
约1分钟内获得全文 去求助
来源期刊
Mathematical Structures in Computer Science
Mathematical Structures in Computer Science 工程技术-计算机:理论方法
CiteScore
1.50
自引率
0.00%
发文量
30
审稿时长
12 months
期刊介绍: Mathematical Structures in Computer Science is a journal of theoretical computer science which focuses on the application of ideas from the structural side of mathematics and mathematical logic to computer science. The journal aims to bridge the gap between theoretical contributions and software design, publishing original papers of a high standard and broad surveys with original perspectives in all areas of computing, provided that ideas or results from logic, algebra, geometry, category theory or other areas of logic and mathematics form a basis for the work. The journal welcomes applications to computing based on the use of specific mathematical structures (e.g. topological and order-theoretic structures) as well as on proof-theoretic notions or results.
期刊最新文献
On Hofmann–Streicher universes T0-spaces and the lower topology GADTs are not (Even partial) functors A linear linear lambda-calculus Countability constraints in order-theoretic approaches to computability
×
引用
GB/T 7714-2015
复制
MLA
复制
APA
复制
导出至
BibTeX EndNote RefMan NoteFirst NoteExpress
×
×
提示
您的信息不完整,为了账户安全,请先补充。
现在去补充
×
提示
您因"违规操作"
具体请查看互助需知
我知道了
×
提示
现在去查看 取消
×
提示
确定
0
微信
客服QQ
Book学术公众号 扫码关注我们
反馈
×
意见反馈
请填写您的意见或建议
请填写您的手机或邮箱
已复制链接
已复制链接
快去分享给好友吧!
我知道了
×
扫码分享
扫码分享
Book学术官方微信
Book学术文献互助
Book学术文献互助群
群 号:481959085
Book学术
文献互助 智能选刊 最新文献 互助须知 联系我们:info@booksci.cn
Book学术提供免费学术资源搜索服务,方便国内外学者检索中英文文献。致力于提供最便捷和优质的服务体验。
Copyright © 2023 Book学术 All rights reserved.
ghs 京公网安备 11010802042870号 京ICP备2023020795号-1