Class Description

compNP: Competitive NP Proof System

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.

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Coh: Coherent Languages

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.

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compIP: Competitive IP Proof System

Same as compNP but for interactive (IP) proofs instead of NP proofs.

More formally, compIP is the class of decision problems L in IP = PSPACE such that, if the answer is "yes," then that can be proven by an interactive protocol between a BPP verifier and a prover, a BPP machine with access only to an oracle for L.

Assuming NEE is not contained in BPEE, NP (and indeed NPCoh) is not contained in compIP [BG94].

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