有限$\mathbb{N}^d$集上受控坏序列的复杂性
Complexity of controlled bad sequences over finite sets of $\mathbb{N}^d$
摘要：
我们提供了控制坏序列的长度的上限和下限的有限集的$\mathbb{N}^d$的主次顺序。这些结果是通过限制这些序列的长度从Cichon层次的功能。这使我们能够将这些结果转换为快速增长的复杂性类的边界。所得到的界限被证明是紧的majoring排序，解决了一个问题留下的开放的Abriola，Figueira和Senno（Theor。Sci，第603卷）。最后，我们利用控制坏序列的结果证明了几类自动机空性问题的上界。
英文摘要：
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.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
