For regular expressions in (strong) star normal form a large set of efficient algorithms is known, from conversions into finite automata to characterisations of unambiguity. In this paper we study the average complexity of this class of expressions using analytic combinatorics. As it is not always feasible to obtain explicit expressions for the generating functions involved, here we show how to get the required information for the asymptotic estimates with an indirect use of the existence of Puiseux expansions at singularities. We study, asymptotically and on average, the alphabetic size, the size of the [Formula: see text]-follow automaton and of the position automaton, as well as the ratio and the size of these expressions to standard regular expressions.

中文翻译：

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强星范式中正则表达式的平均行为

对于（强）星范式中的正则表达式，已知大量有效的算法，从转换为有限自动机到明确性的表征。在本文中，我们使用解析组合学研究此类表达式的平均复杂度。由于获得所涉及的生成函数的显式表达式并不总是可行的，因此我们在这里展示如何通过在奇点处间接使用 Puiseux 展开的存在来获得渐近估计所需的信息。我们渐近平均地研究字母大小、[公式：见文本]跟随自动机和位置自动机的大小，以及这些表达式与标准正则表达式的比率和大小。