Probabilistic Autoreductions
نویسندگان
چکیده
We consider autoreducibility of complete sets for the two common types of probabilistic polynomial-time reductions: RP reductions containing one-sided errors on positive input instances only, and BPP reductions containing two-sided errors. Specifically, we focus on the probabilistic counterparts of the deterministic many-one and truthtable autoreductions. We prove that non-trivial complete sets of NP are autoreducible for the RP many-one reduction. This extends the result by Glaßer et al. (2007) that complete sets of NP are autoreducible for the deterministic many-one reduction. We also prove that complete sets of classes in the truth-table Polynomial Hierarchy, which is the polynomial hierarchy defined using the truth-table reduction instead of the general Turing reduction, are autoreducible with respect to the BPP truth-table reductions. This generalizes the result by Buhrman et. al. (2000) that truth-table-complete sets for NP are probabilistically truth-table autoreducible to multiple classes of higher complexity although for a weaker reduction.
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