Abstract
We show that the class AM∩coAM is low for ZPP NP. As a consequence, it follows that Graph Isomorphism and several group-theoretic problems are low for ZPP NP. We also show that the class IP[P/poly], consisting of sets that have interactive proof systems with honest provers in P/poly, is also low for ZPP NP. For the nonuniform function classes NPMV/poly, NPSV/poly, and NPMV t /poly, we show the following lowness results: Sets whose characteristic functions are in NPSV/poly and that have program checkers are low for AM and ZPP NP. Self-reducible sets with characteristic functions in NPMV t /poly are low for Σ 2 p . Sets whose characteristic functions are in NPMV/poly and that have program checkers are low for Σ 2 p . We also give applications of these lowness results.
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