Abstract
In this paper, we introduce the split game, a variant of the Ehrenfeucht–Fraïssé game from logic, which is useful for analyzing the expressive power of classes of generalized regular expressions. An extension of the split game to generalized ω -regular expressions is also established. To gain insight into how the split game can be applied to attack the long-standing generalized star height 2 problem, we propose and solve the omega power problem, a similar but tractable problem in the context of ω -languages. Namely we show that omega powers, together with boolean combinations and concatenations, are not sufficient to express the class of ω -regular languages.
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