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Can a deterministic finite state transducer output ϵ (epsilon) ?

A Deterministic Finite-state Transducer (DFT) is a device much like a DFA, except that its purpose is not to accept strings or languages but to transform input strings into output strings. Informally, it starts in a designated initial state & moves from state to state , depending on the input , just as DFA does. On each step, however it emits a string of the symbols of the alphabet (zero or one or more than one symbols)depending on the current state & the input symbol. The state diagram of a DFT looks like that of a DFA, except that the label on an arrow looks like a/w, which means “if the input symbol is a, follow this arrow and emit output w”.

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    $\begingroup$ Please acknowledge the source of the text you've quoted. $\endgroup$ – David Richerby Mar 10 '17 at 10:58
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The quote says that the machine emits "zero or one or more than one symbols". Emitting zero symbols is emitting $\varepsilon$.

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