  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.
