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We show the first unconditional pseudo-determinism result for all ofsearch-BPP. Specifically, we show that every BPP search problem can be computedpseudo-deterministically on average for infinitely many input lengths. In otherwords, for infinitely many input lengths and for any polynomial-time samplabledistribution our algorithm succeeds in producing a unique answer (if oneexists) with high probability over the distribution and the coins tossed.

A Note on Unconditional Subexponential-time Pseudo-deterministic Algorithms for BPP Search Problems