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Computer Science > Formal Languages and Automata Theory

arXiv:2308.06683 (cs)
[Submitted on 13 Aug 2023]

Title:Sweep Complexity Revisited

Authors:Szilárd Zsolt Fazekas, Robert Mercaş
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Abstract:We study the sweep complexity of DFA in one-way jumping mode answering several questions posed earlier. This measure is the number of times in the worst case that such machines have to return to the beginning of their input after having skipped some of the symbols. The class of languages accepted by these machines strictly includes the regular class and constant sweep complexity allows exactly the acceptance of regular languages. However, we show that there exist machines with higher than constant complexity still only accepting regular languages and that in general the sweep complexity of an automaton does not distinguish between accepting regular and non-regular languages. We establish separation results for asymptotic classes defined by this complexity measure and give a surprising exponential/logarithmic relation between factors of certain inputs which can be verified by such machines.
Comments: 12 pages, 8 figures
Subjects: Formal Languages and Automata Theory (cs.FL)
MSC classes: 68Q45
ACM classes: F.1.1
Cite as: arXiv:2308.06683 [cs.FL]
  (or arXiv:2308.06683v1 [cs.FL] for this version)
  https://doi.org/10.48550/arXiv.2308.06683

Submission history

From: Szilard Fazekas [view email]
[v1] Sun, 13 Aug 2023 05:02:04 UTC (24 KB)
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