Abstract interpretation from Büchi automata

Proceedings of the Joint Meeting of the Twenty-Third EACSL Annual Conference on Computer Science Logic (CSL) and the Twenty-Ninth Annual ACM/IEEE Symposium on Logic in Computer Science (LICS) Pub Date : 2014-07-14 DOI:10.1145/2603088.2603127

M. Hofmann, Wei Chen

{"title":"Abstract interpretation from Büchi automata","authors":"M. Hofmann, Wei Chen","doi":"10.1145/2603088.2603127","DOIUrl":null,"url":null,"abstract":"We describe the construction of an abstract lattice from a given Buchi automata. The abstract lattice is finite and has the following key properties. (i) There is a Galois connection between it and the (infinite) lattice of languages of finite and infinite words over a given alphabet. (ii) The abstraction is faithful with respect to acceptance by the automaton. (iii) Least fixpoints and ω-iterations (but not in general greatest fixpoints) can be computed on the level of the abstract lattice. This allows one to develop an abstract interpretation capable of checking whether finite and infinite traces of a (recursive) program are accepted by a policy automaton. It is also possible to cast this analysis in form of a type and effect system with the effects being elements of the abstract lattice. While the resulting decidability and complexity results are known (regular model checking for pushdown systems) the abstract lattice provides a new point of view and enables smooth integration with data types, objects, higher-order functions which are best handled with abstract interpretation or type systems. We demonstrate this by generalising our type-and-effect systems to object-oriented programs and higher-order functions.","PeriodicalId":20649,"journal":{"name":"Proceedings of the Joint Meeting of the Twenty-Third EACSL Annual Conference on Computer Science Logic (CSL) and the Twenty-Ninth Annual ACM/IEEE Symposium on Logic in Computer Science (LICS)","volume":"6 1","pages":""},"PeriodicalIF":0.0000,"publicationDate":"2014-07-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"32","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Proceedings of the Joint Meeting of the Twenty-Third EACSL Annual Conference on Computer Science Logic (CSL) and the Twenty-Ninth Annual ACM/IEEE Symposium on Logic in Computer Science (LICS)","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1145/2603088.2603127","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}

引用次数: 32

Abstract

We describe the construction of an abstract lattice from a given Buchi automata. The abstract lattice is finite and has the following key properties. (i) There is a Galois connection between it and the (infinite) lattice of languages of finite and infinite words over a given alphabet. (ii) The abstraction is faithful with respect to acceptance by the automaton. (iii) Least fixpoints and ω-iterations (but not in general greatest fixpoints) can be computed on the level of the abstract lattice. This allows one to develop an abstract interpretation capable of checking whether finite and infinite traces of a (recursive) program are accepted by a policy automaton. It is also possible to cast this analysis in form of a type and effect system with the effects being elements of the abstract lattice. While the resulting decidability and complexity results are known (regular model checking for pushdown systems) the abstract lattice provides a new point of view and enables smooth integration with data types, objects, higher-order functions which are best handled with abstract interpretation or type systems. We demonstrate this by generalising our type-and-effect systems to object-oriented programs and higher-order functions.

查看原文本刊更多论文

从气自动机的抽象解释

我们描述了一个给定布吉自动机的抽象格的构造。抽象格是有限的，并具有以下关键性质。(1)在给定的字母表上，它与有限词和无限词的语言的(无限)格之间存在伽罗瓦联系。(二)抽象对于自动机的接受是忠实的。(iii)最小不动点和ω-迭代(但一般不是最大不动点)可以在抽象格的水平上计算。这允许开发一种抽象解释，能够检查(递归)程序的有限和无限轨迹是否被策略自动机所接受。也可以将这种分析以类型和效果系统的形式进行，其中效果是抽象晶格的元素。虽然最终的可判定性和复杂性结果是已知的(对下推系统进行常规的模型检查)，但抽象晶格提供了一个新的观点，并支持与数据类型、对象、高阶函数的平滑集成，这些最好通过抽象解释或类型系统来处理。我们通过将类型和效果系统推广到面向对象程序和高阶函数来证明这一点。

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分钟内获得全文求助全文

来源期刊

Proceedings of the Joint Meeting of the Twenty-Third EACSL Annual Conference on Computer Science Logic (CSL) and the Twenty-Ninth Annual ACM/IEEE Symposium on Logic in Computer Science (LICS)

自引率

0.00%

发文量