The Complexity of Positive First-order Logic without Equality

B. Martin, Jos Martin
{"title":"The Complexity of Positive First-order Logic without Equality","authors":"B. Martin, Jos Martin","doi":"10.1145/2071368.2071373","DOIUrl":null,"url":null,"abstract":"We study the complexity of evaluating positive equality-free sentences of first-order (FO) logic over a fixed, finite structure B. This may be seen as a natural generalisation of the non-uniform quantified constraint satisfaction problem QCSP(B). We introduce surjective hyper-endomorphisms and use them in proving a Galois connection that characterises definability in positive equality-free FO. Through an algebraic method, we derive a complete complexity classification for our problems as B ranges over structures of size at most three. Specifically, each problem is either in Logspace, is NP-complete, is coNP-complete or is Pspace-complete.","PeriodicalId":415902,"journal":{"name":"2009 24th Annual IEEE Symposium on Logic In Computer Science","volume":"1 1","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"2009-08-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"11","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"2009 24th Annual IEEE Symposium on Logic In Computer Science","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1145/2071368.2071373","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 11

Abstract

We study the complexity of evaluating positive equality-free sentences of first-order (FO) logic over a fixed, finite structure B. This may be seen as a natural generalisation of the non-uniform quantified constraint satisfaction problem QCSP(B). We introduce surjective hyper-endomorphisms and use them in proving a Galois connection that characterises definability in positive equality-free FO. Through an algebraic method, we derive a complete complexity classification for our problems as B ranges over structures of size at most three. Specifically, each problem is either in Logspace, is NP-complete, is coNP-complete or is Pspace-complete.
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
不相等的正一阶逻辑的复杂性
我们研究了在一个固定的有限结构B上评价一阶(FO)逻辑的无等正句子的复杂性,这可以看作是非一致量化约束满足问题QCSP(B)的自然推广。我们引入了满射超自同态,并利用它们证明了一个伽罗瓦连接,该伽罗瓦连接表征了无正相等FO中的可定义性。通过一种代数方法,我们得到了我们的问题的一个完全的复杂性分类,即B范围的结构的大小最多为3。具体来说,每个问题要么在Logspace中,要么是np完全的,要么是cp完全的,要么是p空间完全的。
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
自引率
0.00%
发文量
0
期刊最新文献
Applications of Game Semantics: From Program Analysis to Hardware Synthesis Fully Abstract Logical Bisimilarity for a Polymorphic Object Calculus The Inverse Taylor Expansion Problem in Linear Logic Logical Step-Indexed Logical Relations Quantitative Model Checking of Continuous-Time Markov Chains Against Timed Automata Specifications
×
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