Complexity of controlled bad sequences over finite sets of N^k
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We provide lower and upper bounds for the length of controlled bad sequences over the majoring and the minoring orderings for finite sets of N^k. The results are obtained by bounding the length of such sequences by functions from the Cichon hierarchy. This also allows us to translate these results to bounds over the fast-growing complexity classes. The obtained bounds are proven to be tight for the majoring ordering.
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