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A finite-state transducer is a generalization of a finite state machine that accepts an input string and produces an output string (instead of just accepting or rejecting). Is there a name for a function $f : \Sigma_1^* \rightarrow \Sigma_2^*$ that can be computed by a finite-state transducer? Functions of this form computable by Turing machines are typically called computable functions, and I was curious if there was an analogous term for FSTs.

Thanks!

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It's called a Finite state transduc$tion$.

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