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A reduction is the transformation of one problem into another problem. A example of using a reduction would be to be to show if a problem P is undecidable. This would be achieved by transforming or performing a reduction of a decision problem $P$ into an undecidable problem. If this can be achieved then we have shown that this problem P is undecidable.
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What is the relationship between $\mathsf{L}$ reductions and $\mathsf{NC}$ reductions?
$\mathsf{P}$-completeness may be defined using either $\mathsf{NC}$ reductions or $\mathsf{L}$ reductions. … What separations or equivalences are known between these two types of reductions? …