Logspace many-one reduction ($A{\le }_m^{\log }B$)

A total mapping $f$ with $x\in A$ exactly when $f(x)\in B$, computed by a deterministic logarithmic-work-space transducer with read-only input and write-only output. Such reductions compose, and are used for NL-completeness and P-completeness. The output can be polynomially larger than the work storage.