Transducing Reversibly with Finite State Machines
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Finite state machines are investigated towards their ability to reversibly compute transductions, that is, to transform inputs into outputs in a reversible way. This means that the transducers are backward deterministic and hence are able to uniquely step the computation back and forth. The families of transductions computed are classified with regard to three types of length-preserving transductions as well as to the property of working reversibly. It is possible to settle all inclusion relations between the families of transductions. Finally, the standard closure properties are investigated and the non-closure under almost all operations can be shown.
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