An iterated uniform finite-state transducer executes the same length-preserving transduction in iterative sweeps. The first sweep occurs on the input string, while any subsequent sweep works on the output of the previous one. We consider devices with one-way motion and two-way motion, i.e., sweeps are either from left to right only, or alternate from left to right and from right to left. In addition, devices may work deter-ministically or nondeterministically. Here, we restrict to study devices performing a constant number of sweeps, which are known to characterize exactly the regular languages. We determine the descriptional costs of removing two-way motion, nondeterminism, and sweeps, and, in particular, the costs for the conversion to deterministic or nondeterministic finite automata. Finally, the special case of unary languages is investigated, and a language family is presented that is immune to the resources of nondeterminism and two-way motion, in the sense that both resources can neither reduce the number of states nor the number of sweeps.
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