The class of omega languages recognized by deterministic parity acceptors (DPAs) or deterministic Muller acceptors (DMAs) is exactly the regular omega languages. The inclusion problem is the following: given two acceptors A1 and A2, determine whether the language recognized by A1 is a subset of the language recognized by A2, and if not, return an ultimately periodic omega word accepted by A1 but not A2. We describe polynomial time algorithms to solve this problem for two DPAs and for two DMAs. Corollaries include polynomial time algorithms to solve the equivalence problem for DPAs and DMAs, and also the inclusion and equivalence problems for deterministic Buechi and coBuechi acceptors.

中文翻译：

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确定性 omega 受体的包含和等价的多项式时间算法

确定性奇偶校验接受器 (DPA) 或确定性穆勒接受器 (DMA) 识别的 omega 语言类别正是常规的 omega 语言。包含问题如下：给定两个接受器 A1 和 A2，判断 A1 识别的语言是否是 A2 识别的语言的子集，如果不是，则返回一个最终周期的 omega 词被 A1 接受但不是 A2。我们描述了多项式时间算法来解决两个 DPA 和两个 DMA 的问题。推论包括解决 DPA 和 DMA 等价问题的多项式时间算法，以及确定性 Buechi 和 coBuechi 接受器的包含和等价问题。