In this article, we study some properties of random regular expressions of size n, when the cardinality of the alphabet also depends on n. For this, we revisit and improve the classical Transfer Theorem from the field of analytic combinatorics. This provides precise estimations for the number of regular expressions, the probability of recognizing the empty word and the expected number of Kleene stars in a random expression. For all these statistics, we show that there is a threshold when the size of the alphabet approaches n2, at which point the leading term in the asymptotics starts oscillating.

中文翻译：

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大字母上的随机正则表达式

在本文中，我们研究了大小随机正则表达式的一些性质n, 当字母表的基数也取决于n. 为此，我们从分析组合学领域重新审视和改进了经典的转移定理。这为正则表达式的数量、识别空词的概率和随机表达式中的预期 Kleene 星数提供了精确的估计。对于所有这些统计数据，我们表明当字母表的大小接近时存在阈值n2，此时渐近线中的前导项开始振荡。