Brzozowski introduced the notion of derivatives for regular expressions. They can be used for a very simple regular expression matching algorithm. Sulzmann and Lu cleverly extended this algorithm in order to deal with POSIX matching, which is the underlying disambiguation strategy for regular expressions needed in lexers. Their algorithm generates POSIX values which encode the information of how a regular expression matches a string—that is, which part of the string is matched by which part of the regular expression. In this paper we give our inductive definition of what a POSIX value is and show that Sulzmann and Lu’s algorithm always generates such a value. We also show that our inductive definition of a POSIX value is equivalent to an alternative definition by Okui and Suzuki which identifies POSIX values as least elements according to an ordering of values.

Brzozowski 引入了正则表达式导数的概念。它们可用于非常简单的正则表达式匹配算法。Sulzmann 和 Lu 巧妙地扩展了该算法，以处理 POSIX 匹配，这是词法分析器所需的正则表达式的基础消歧策略。他们的算法生成 POSIX 值，这些值对如何进行编码的信息进行编码正则表达式匹配字符串，即字符串的哪一部分与正则表达式的哪一部分匹配。在本文中，我们给出了 POSIX 值的归纳定义，并表明 Sulzmann 和 Lu 的算法总是生成这样的值。我们还表明，我们对 POSIX 值的归纳定义相当于 Okui 和 Suzuki 的替代定义，后者根据值的顺序将 POSIX 值识别​​为最小元素。