Abstract
In this paper, we consider two-way transducers with a two-way output tape. To each cell of the input tape corresponds a cell of the output tape where the transducer can write a finite word. At each transition, the transducer reads one cell of the input tape and either leave unchanged the corresponding cell of the output tape or write a new word into it, overwriting the previous content. We show that each relation realized by such a two-way transducer is rational. It can be realized by a one-way transducer. We also show that any rational function can be realized by a deterministic two-way transducer.
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