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In computational complexity theory, a log-space computable function is a function ${\displaystyle f\colon \Sigma ^{\ast }\rightarrow \Sigma ^{\ast }}$ that requires only ${\displaystyle O(\log n)}$ memory to be computed (this restriction does not apply to the size of the output). The computation is generally done by means of a log-space transducer.

Log-space reductions

The main use for log-space computable functions is in log-space reductions. This is a means of transforming an instance of one problem into an instance of another problem, using only logarithmic space.

Examples of log-space computable functions

• Function converting a problem of a non-deterministic Turing machine that decides a language A in log-space to ST-connectivity.

Notes

1. Sipser (2006) International Second Edition, p. 328.

References

• Sipser, Michael (2006), Introduction to the Theory of Computation, Cengage Learning, ISBN 978-0-619-21764-8.

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