Computer Science > Logic in Computer Science
[Submitted on 4 Sep 2019 (v1), last revised 8 Jun 2020 (this version, v5)]
Title:Complexity of controlled bad sequences over finite sets of $\mathbb{N}^d$
View PDFAbstract: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.
Submission history
From: Balasubramanian A.R [view email][v1] Wed, 4 Sep 2019 09:58:31 UTC (23 KB)
[v2] Sun, 8 Sep 2019 16:15:01 UTC (23 KB)
[v3] Fri, 13 Sep 2019 19:59:17 UTC (23 KB)
[v4] Tue, 14 Jan 2020 10:30:08 UTC (72 KB)
[v5] Mon, 8 Jun 2020 10:21:46 UTC (76 KB)
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