On ω-regular sets

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The investigation of the acceptional power of finite automata with respect to several notions of acceptance for ω-sets, done in the literature, has exhibited six subclasses of the class of ω-regular sets. These classes are well characterized by means of topology and set representation. First we give an overview of these results. The main aim of this paper is the investigation of further natural subclasses of the class of ω-regular sets. We define such subclasses by three methods: by the structural complexity of accepting automata, by the m-reducibility with finite automata, and by topological difficulty. It turns out that these classifications coincide or are at least comparable to each other.

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