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The Rabin index of a rational language of infinite words given by a
parity automaton with states is computable in time (
) where
is the cardinality of the alphabet. The number of values used by a
parity acceptance condition is always greater than the Rabin index and
conversely, the acceptance condition of a parity automaton can always be
replaced by an equivalent acceptance condition whose number of used
values is exactly the Rabin index. This new acceptance...
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