Regular Expressions (REs) are ubiquitous in database and programming languages. While many applications make use of REs extended with interleaving ( shuffle ) and unordered concatenation operators, this extension badly affects the complexity of basic operations, and, especially, makes membership NP-hard, which is unacceptable in most practical scenarios. In this article, we study the problem of membership checking for a restricted class of these extended REs, called conflict-free REs , which are expressive enough to cover the vast majority of real-world applications. We present several polynomial algorithms for membership checking over conflict-free REs. The algorithms are all polynomial and differ in terms of adopted optimization techniques and in the kind of supported operators. As a particular application, we generalize the approach to check membership of Extensible Markup Language trees into a class of EDTDs (Extended Document Type Definitions) that models the crucial aspects of DTDs (Document Type Definitions) and XSD (XML Schema Definitions) schemas. Results about an extensive experimental analysis validate the efficiency of the presented membership checking techniques.

中文翻译：

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一类具有计数、交错和无序连接的正则表达式中的线性时间隶属度

正则表达式 (RE) 在数据库和编程语言中无处不在。虽然许多应用程序使用扩展的 RE交错(洗牌） 和无序连接操作符，这种扩展严重影响了基本操作的复杂性，尤其是会员资格NP-hard，在大多数实际场景中是不可接受的。在本文中，我们研究了这些扩展 RE 的受限类的成员资格检查问题，称为无冲突的 RE，它们的表现力足以涵盖绝大多数现实世界的应用程序。我们提出了几种用于对无冲突 RE 进行成员资格检查的多项式算法。这些算法都是多项式的，并且在采用的优化技术和支持的运算符类型方面有所不同。作为一个特定的应用程序，我们将检查可扩展标记语言树的成员资格的方法概括为一类 EDTD（扩展文档类型定义），该类对 DTD（文档类型定义）和 XSD（XML 模式定义）模式的关键方面进行建模。关于广泛的实验分析的结果验证了所提出的成员检查技术的效率。