Log-space transducer

A log space transducer (LST) is a type of Turing machine used for log-space reductions.

A log space transducer, ${\displaystyle M}$, has three tapes:

${\displaystyle M}$ will be designed to compute a log-space computable function ${\displaystyle f\colon \Sigma ^{\ast }\rightarrow \Sigma ^{\ast }}$ (where ${\displaystyle \Sigma }$ is the alphabet of both the input and output tapes). If ${\displaystyle M}$ is executed with ${\displaystyle w}$ on its input tape, when the machine halts, it will have ${\displaystyle f(w)}$ remaining on its output tape.

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