On Closure Properties of Bounded 2-Sided Error Complexity Classes
نویسندگان
چکیده
We show that if a complexity class C is closed downward under polynomialtime majority truth-table reductions (≤pmtt), then practically every other “polynomial” closure property it enjoys is inherited by the corresponding bounded 2-sided error class BP[C]. For instance, the Arthur-Merlin game class AM [Bab85] enjoys practically every closure property of NP. Our main lemma shows that for any relativizable class D which meets two fairly transparent technical conditions, we have DBP[C] ⊆ BP[D C ]. Among our applications, we simplify the proof by S. Toda [Tod89, Tod91] that the polynomial hierarchy PH is contained in BP[⊕P]. We also show that relative to a random oracle R, PH is properly contained in ⊕P.
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