概率正则图

Infinity Pub Date : 2010-10-28 DOI:10.4204/EPTCS.39.6
N. Bertrand, Christophe Morvan
{"title":"概率正则图","authors":"N. Bertrand, Christophe Morvan","doi":"10.4204/EPTCS.39.6","DOIUrl":null,"url":null,"abstract":"Deterministic graph grammars generate regular graphs, that form a structural extension of configuration graphs of pushdown systems. In this paper, we study a probabilistic extension of regular graphs obtained by labelling the terminal arcs of the graph grammars by probabilities. Stochastic properties of these graphs are expressed using PCTL, a probabilistic extension of computation tree logic. We present here an algorithm to perform approximate verification of PCTL formulae. Moreover, we prove that the exact model-checking problem for PCTL on probabilistic regular graphs is undecidable, unless restricting to qualitative properties. Our results generalise those of EKM06, on probabilistic pushdown automata, using similar methods combined with graph grammars techniques.","PeriodicalId":31175,"journal":{"name":"Infinity","volume":"17 1","pages":"77-90"},"PeriodicalIF":0.0000,"publicationDate":"2010-10-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"4","resultStr":"{\"title\":\"Probabilistic regular graphs\",\"authors\":\"N. Bertrand, Christophe Morvan\",\"doi\":\"10.4204/EPTCS.39.6\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"Deterministic graph grammars generate regular graphs, that form a structural extension of configuration graphs of pushdown systems. In this paper, we study a probabilistic extension of regular graphs obtained by labelling the terminal arcs of the graph grammars by probabilities. Stochastic properties of these graphs are expressed using PCTL, a probabilistic extension of computation tree logic. We present here an algorithm to perform approximate verification of PCTL formulae. Moreover, we prove that the exact model-checking problem for PCTL on probabilistic regular graphs is undecidable, unless restricting to qualitative properties. Our results generalise those of EKM06, on probabilistic pushdown automata, using similar methods combined with graph grammars techniques.\",\"PeriodicalId\":31175,\"journal\":{\"name\":\"Infinity\",\"volume\":\"17 1\",\"pages\":\"77-90\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2010-10-28\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"4\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Infinity\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.4204/EPTCS.39.6\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Infinity","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.4204/EPTCS.39.6","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 4

摘要

确定性图语法生成规则图,规则图是下推系统组态图的结构扩展。本文研究了正则图的一种概率扩展,该扩展是用概率标记正则图语法的端点弧得到的。这些图的随机性质用PCTL表示,PCTL是计算树逻辑的一种概率扩展。我们在此提出一种算法来执行PCTL公式的近似验证。此外,我们还证明了概率正则图上PCTL的精确模型检验问题是不确定的,除非局限于定性性质。我们的结果推广了EKM06的结果,在概率下推自动机上,使用类似的方法结合图语法技术。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
Probabilistic regular graphs
Deterministic graph grammars generate regular graphs, that form a structural extension of configuration graphs of pushdown systems. In this paper, we study a probabilistic extension of regular graphs obtained by labelling the terminal arcs of the graph grammars by probabilities. Stochastic properties of these graphs are expressed using PCTL, a probabilistic extension of computation tree logic. We present here an algorithm to perform approximate verification of PCTL formulae. Moreover, we prove that the exact model-checking problem for PCTL on probabilistic regular graphs is undecidable, unless restricting to qualitative properties. Our results generalise those of EKM06, on probabilistic pushdown automata, using similar methods combined with graph grammars techniques.
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
CiteScore
2.30
自引率
0.00%
发文量
26
审稿时长
10 weeks
×
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