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.

翻译：我们为正则表达式展示了一个名为公式大小游戏的版本。 这些游戏将语言的等值描述为给定大小的表达式。 我们使用正则表达式规模游戏来简单证明一阶逻辑和正则表达式之间已知的非基本简洁性差距。 我们还使用游戏只用一个表达式来计算恒星数量而不是总体大小。 对于常规表达式来说,这种测量方式在表达力方面轻描淡写地给出了等级分级。 对于我们所说的无恒表达式而言,我们也获得了这样的等级。 在那里,没有恒星的表达式是补充的,但没有恒星的表达式是使用正则表达式的操作组合的。