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We consider reversible and surjective cellular automata perturbed with noise.We show that, in the presence of positive additive noise, the cellularautomaton forgets all the information regarding its initial configurationexponentially fast. In particular, the state of a finite collection of cellswith diameter n becomes indistinguishable from pure noise after O(log n) timesteps. This highlights the seemingly unavoidable need for irreversibility inorder to perform scalable reliable computation in the presence of noise.

Reversible cellular automata in presence of noise rapidly forget everything