顺序性,一元二阶逻辑和树自动机

IF 0.7 4区 物理与天体物理 Q3 COMPUTER SCIENCE, THEORY & METHODS
H. Comon
{"title":"顺序性,一元二阶逻辑和树自动机","authors":"H. Comon","doi":"10.1006/INCO.1999.2838","DOIUrl":null,"url":null,"abstract":"Abstract Given a term rewriting system R and a normalizable term t, a redex is needed if in any reduction sequence of t to a normal form, this redex will be contracted. Roughly, R is sequential if there is an optimal reduction strategy in which only needed redexes are contracted. More generally, G. Huet and J.-J. Levy have defined the sequentiality of a predicate P on partially evaluated terms (1991, “Computational Logic: Essays in Honor of Alan Robinson”, MIT Press, Cambridge, MA, pp. 415–443). We show here that the sequentiality of P is definable in SkS, the monadic second-order logic with k successors, provided P is definable in SkS. We derive several known and new consequences of this remark: (1) strong sequentiality, as defined by Huet and Levy of a left linear (possibly overlapping) rewrite system is decidable, (2) NV-sequentiality, as defined in (M. Oyamaguchi, 1993, SIAM J. Comput.19, 424–437), is decidable, even in the case of overlapping rewrite systems (3) sequentiality of any linear shallow rewrite system is decidable. Then we describe a direct construction of a tree automaton recognizing the set of terms that do have needed redexes, which again, yields immediate consequences: (1) Strong sequentiality of possibly overlapping linear rewrite systems is decidable in EXPTIME, (2) For strongly sequential rewrite systems, needed redexes can be read directly on the automaton.","PeriodicalId":54524,"journal":{"name":"Quantum Information & Computation","volume":null,"pages":null},"PeriodicalIF":0.7000,"publicationDate":"2000-02-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"25","resultStr":"{\"title\":\"Sequentiality, monadic second-order logic and tree automata\",\"authors\":\"H. Comon\",\"doi\":\"10.1006/INCO.1999.2838\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"Abstract Given a term rewriting system R and a normalizable term t, a redex is needed if in any reduction sequence of t to a normal form, this redex will be contracted. Roughly, R is sequential if there is an optimal reduction strategy in which only needed redexes are contracted. More generally, G. Huet and J.-J. Levy have defined the sequentiality of a predicate P on partially evaluated terms (1991, “Computational Logic: Essays in Honor of Alan Robinson”, MIT Press, Cambridge, MA, pp. 415–443). We show here that the sequentiality of P is definable in SkS, the monadic second-order logic with k successors, provided P is definable in SkS. We derive several known and new consequences of this remark: (1) strong sequentiality, as defined by Huet and Levy of a left linear (possibly overlapping) rewrite system is decidable, (2) NV-sequentiality, as defined in (M. Oyamaguchi, 1993, SIAM J. Comput.19, 424–437), is decidable, even in the case of overlapping rewrite systems (3) sequentiality of any linear shallow rewrite system is decidable. Then we describe a direct construction of a tree automaton recognizing the set of terms that do have needed redexes, which again, yields immediate consequences: (1) Strong sequentiality of possibly overlapping linear rewrite systems is decidable in EXPTIME, (2) For strongly sequential rewrite systems, needed redexes can be read directly on the automaton.\",\"PeriodicalId\":54524,\"journal\":{\"name\":\"Quantum Information & Computation\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":0.7000,\"publicationDate\":\"2000-02-25\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"25\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Quantum Information & Computation\",\"FirstCategoryId\":\"101\",\"ListUrlMain\":\"https://doi.org/10.1006/INCO.1999.2838\",\"RegionNum\":4,\"RegionCategory\":\"物理与天体物理\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q3\",\"JCRName\":\"COMPUTER SCIENCE, THEORY & METHODS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Quantum Information & Computation","FirstCategoryId":"101","ListUrlMain":"https://doi.org/10.1006/INCO.1999.2838","RegionNum":4,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"COMPUTER SCIENCE, THEORY & METHODS","Score":null,"Total":0}
引用次数: 25

摘要

摘要给定一个项重写系统R和一个可归一化的项t,如果在任何一个将t约简为正规形式的序列中,该索引将被缩约,则需要一个索引。粗略地说,如果存在只收缩所需索引的最优缩减策略,则R是顺序的。更一般地说,G. Huet和J.-J。Levy在部分求值项上定义了谓词P的顺序性(1991,“计算逻辑:纪念艾伦·罗宾逊的论文”,麻省理工学院出版社,剑桥,麻萨诸塞州,第415-443页)。我们证明了如果P在SkS中是可定义的,那么P的序性在SkS中是可定义的,即具有k个后继的一元二阶逻辑。我们得到了几个已知的和新的结论:(1)Huet和Levy定义的左线性(可能重叠)重写系统的强序性是可决定的;(2)nv序性,如(M. yamaguchi, 1993, SIAM J. computer .19, 424-437)中定义的,即使在重叠重写系统的情况下也是可决定的;(3)任何线性浅重写系统的序性是可决定的。然后,我们描述了一个树自动机的直接构造,该树自动机识别具有所需索引的术语集,这再次产生了直接的结果:(1)可能重叠的线性重写系统的强顺序性在EXPTIME中是可确定的;(2)对于强顺序重写系统,所需索引可以直接在自动机上读取。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
Sequentiality, monadic second-order logic and tree automata
Abstract Given a term rewriting system R and a normalizable term t, a redex is needed if in any reduction sequence of t to a normal form, this redex will be contracted. Roughly, R is sequential if there is an optimal reduction strategy in which only needed redexes are contracted. More generally, G. Huet and J.-J. Levy have defined the sequentiality of a predicate P on partially evaluated terms (1991, “Computational Logic: Essays in Honor of Alan Robinson”, MIT Press, Cambridge, MA, pp. 415–443). We show here that the sequentiality of P is definable in SkS, the monadic second-order logic with k successors, provided P is definable in SkS. We derive several known and new consequences of this remark: (1) strong sequentiality, as defined by Huet and Levy of a left linear (possibly overlapping) rewrite system is decidable, (2) NV-sequentiality, as defined in (M. Oyamaguchi, 1993, SIAM J. Comput.19, 424–437), is decidable, even in the case of overlapping rewrite systems (3) sequentiality of any linear shallow rewrite system is decidable. Then we describe a direct construction of a tree automaton recognizing the set of terms that do have needed redexes, which again, yields immediate consequences: (1) Strong sequentiality of possibly overlapping linear rewrite systems is decidable in EXPTIME, (2) For strongly sequential rewrite systems, needed redexes can be read directly on the automaton.
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
Quantum Information & Computation
Quantum Information & Computation 物理-计算机:理论方法
CiteScore
1.70
自引率
0.00%
发文量
42
审稿时长
3.3 months
期刊介绍: Quantum Information & Computation provides a forum for distribution of information in all areas of quantum information processing. Original articles, survey articles, reviews, tutorials, perspectives, and correspondences are all welcome. Computer science, physics and mathematics are covered. Both theory and experiments are included. Illustrative subjects include quantum algorithms, quantum information theory, quantum complexity theory, quantum cryptology, quantum communication and measurements, proposals and experiments on the implementation of quantum computation, communications, and entanglement in all areas of science including ion traps, cavity QED, photons, nuclear magnetic resonance, and solid-state proposals.
×
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
确定
请完成安全验证×
copy
已复制链接
快去分享给好友吧!
我知道了
右上角分享
点击右上角分享
0
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 布克学术 All rights reserved.
京ICP备2023020795号-1
ghs 京公网安备 11010802042870号
Book学术文献互助
Book学术文献互助群
群 号:481959085
Book学术官方微信