Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Complexity of controlled bad sequences over finite sets of
  $\mathbb{N}^d$   We provide upper and lower bounds for the length of controlled bad sequences
over the majoring and the minoring orderings of finite sets of $\mathbb{N}^d$.
The results are obtained by bounding the length of such sequences by functions
from the Cichon hierarchy. This 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, which
solves a problem left open by Abriola, Figueira and Senno (Theor. Comp. Sci,
Vol. 603). Finally, we use the results on controlled bad sequences to prove
upper bounds for the emptiness problem of some classes of automata.

37
The categories of this paper are: supr-con
20
The categories of this paper are: acc-phys
33
The categories of this paper are: plasm-ph
19
The categories of this paper are: eess
8
The categories of this paper are: hep-ex
17
The categories of this paper are: q-fin
21
The categories of this paper are: adap-org
4
The categories of this paper are: cond-mat
28
The categories of this paper are: alg-geom
9
The categories of this paper are: nlin
2
The categories of this paper are: math
15
The categories of this paper are: nucl-ex
32
The categories of this paper are: atom-ph
36
The categories of this paper are: cmp-lg
6
The categories of this paper are: astro-ph
5
The categories of this paper are: gr-qc