Complexity of controlled bad sequences over finite powersets of N^k

09/04/2019

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by   A. R. Balasubramanian, et al.

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We provide lower and upper bounds for the length of controlled bad sequences over the majoring and the minoring ordering for finite powersets 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 tight for the majoring ordering, which solves a problem left open in [Abriola et al, 2015]. Further, to the best of our knowledge this is the first such upper bound provided for the minoring ordering.