We present a version of so called formula size games for regular expressions. These games characterize the equivalence of languages up to expressions of a given size. We use the regular expression size game to give a simple proof of a known non-elementary succinctness gap between first-order logic and regular expressions. We also use the game to only count the number of stars in an expression instead of the overall size. For regular expressions this measure trivially gives a hierarchy in terms of expressive power. We obtain such a hierarchy also for what we call RE over star-free expressions, where star-free expressions, that is ones with complement but no stars, are combined using the operations of regular expressions.

中文翻译：

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正则表达式简洁游戏

我们为正则表达式提供了一个所谓的公式大小游戏的版本。这些游戏表征了语言在给定大小的表达式中的等价性。我们使用正则表达式大小游戏来给出一阶逻辑和正则表达式之间已知的非基本简洁性差距的简单证明。我们还使用游戏只计算表达式中的星星数，而不是整体大小。对于正则表达式，这个度量简单地给出了表达能力方面的层次结构。我们也为我们在无星表达式上称为 RE 获得了这样的层次结构，其中使用正则表达式的操作组合了无星表达式，即有补码但没有星号的表达式。