Class Description

Check: Checkable Languages

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,

1. If P(y)=f(y) for all inputs y, then C^P(x) (C with oracle access to P) accepts with probability at least 2/3.
2. If P(x) is not equal to f(x) then C^P(x) accepts with probability at most 1/3.

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.

Linked From

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.

More about...

QPSPACE: Quasipolynomial-Space

Equals DSPACE(2^polylog(n)).

According to [BG94], Beigel and Feigenbaum and (independently) Krawczyk showed that QPSPACE is not contained in Check.

More about...