Acceptance conditions for omega-languages and the Borel hierarchy

This paper investigates acceptance conditions for finite automata recognizing ω-regular languages. As a first result, we show that, under any acceptance condition that can be defined in the MSO logic, a finite automaton can recognize at most ω-regular languages. Starting from this, the paper aims at classifying acceptance conditions according to their expressive power and at finding the exact position of the classes of ω-languages they induced according to the Borel hierarchy. A new interesting acceptance condition is introduced and fully characterized. A step forward is also made in the understanding of the expressive power of (fin,=).

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