The class of problems L that have a decider in the following sense. There exists a BPP machine D such that for all inputs x,
Contains compIP [BG94] and Check [BK89].
Contained in MIP = NEXP [FRS88].
Assuming NEE is not contained in BPEE, NP (and indeed NP ∩ Coh) is not contained in frIP [BG94].
The class of problems such that a polynomial-time program P that allegedly solves them can be checked efficiently. That is, f is in Check if there exists a BPP algorithm C such that for all programs P and inputs x,
Introduced in [BK89], where it was also shown that Check equals frIP ∩ cofrIP.
Check is contained in NEXP ∩ coNEXP [FRS88].
[BG94] show that if NEE is not contained in BPEE then NP is not contained in Check.
The class of problems L that are efficiently autoreducible, in the sense that given an input x and access to an oracle for L, a BPP machine can compute L(x) by querying L only on points that differ from x.
Defined in [Yao90b].
[BG94] show that, assuming NEE is not contained in BPEE, Coh ∩ NP is not contained in any of compNP, Check, or frIP.
The class of decision problems L in NP such that, if the answer is "yes," then a proof can be constructed in polynomial time given access only to an oracle for L.
Contains NPC.
[BG94] show that compNP is contained in frIP, and that assuming NEE is not contained in BPEE, compNP does not equal NP.