We introduce and initiate the study of a new model of reductions called the random noise model. In this model, the truth table $T_f$ of the function $f$ is corrupted on a randomly chosen $\delta$-fraction of instances. A randomized algorithm $\mathcal{A}$ is a $\left(t, \delta, 1-\varepsilon\right)$-recovery reduction for $f$ if:

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