We present an innovative approach for capturing the complexity of ω-regular languages using the concept of flowers. This semantic tool combines two syntax-based definitions, namely the Mostowski hierarchy of word languages and syntactic flowers. The former is based on deterministic parity automata with a limited number of priorities, while the latter simplifies deterministic parity automata by reducing the number of priorities used, without altering their structure. Synthesising these two approaches yields a semantic concept of flowers, which offers a more effective way of dealing with the complexity of ω-regular languages. This letter provides a comprehensive definition of semantic flowers and shows that it captures the complexity of ω-regular languages. We also show that this natural concept yields simple proofs of the expressive power of good-for-games automata.

我们提出了一种创新方法，利用花的概念来捕捉ω正则语言的复杂性。该语义工具结合了两种基于语法的定义，即单词语言的莫斯托夫斯基层次结构和句法花。前者基于具有有限数量优先级的确定性奇偶校验自动机，而后者通过减少所使用的优先级数量来简化确定性奇偶校验自动机，而不改变其结构。综合这两种方法产生了花的语义概念，它提供了一种更有效的方法来处理ω正则语言的复杂性。这封信提供了语义花的全面定义，并表明它捕获了ω正则语言的复杂性。我们还表明，这个自然概念可以简单证明游戏自动机的表达能力。