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This paper investigates acceptance conditions for finite automata recognizingomega-regular languages. As a first result, we show that, under any acceptancecondition that can be defined in the MSO logic, a finite automaton canrecognize at most omega-regular languages. Starting from this, the paper aimsat classifying acceptance conditions according to their expressive power and atfinding the exact position of the classes of omega-languages they inducedaccording to the Borel hierarchy. A new interesting acceptance condition isintroduced and fully characterized. A step forward is also made in theunderstanding of the expressive power of (fin, =).

Acceptance conditions for omega-languages and the Borel hierarchy