Equals PNP[log] ([BH91] and [Hem89] independently).
Equals the union of DTIME(2p(n)) over all polynomials p.
If EXP is in P/poly then EXP = MA [BFL91].
Problems complete for EXP under many-one reductions have measure 0 in EXP [May94], [JL95].
There exist oracles relative to which
[BT04] show the following rather striking result: let A be many-one complete for EXP, and let S be any set in P of subexponential density. Then A-S is Turing-complete for EXP.
[SM03] show that if EXP has circuits of polynomial size, then P can be simulated in MAPOLYLOG such that no deterministic polynomial-time adversary can generate a list of inputs for a P problem that includes one which fails to be simulated. As a result, EXP ⊆ MA if EXP has circuits of polynomial size.
[SU05] show that EXP NP/poly implies EXP P||NP/poly.
In descriptive complexity EXPTIME can be defined as SO() which is also SO(LFP)
Same as NP/poly, except that now the advice string is logarithmic-size.
Shown in [FK05] that EXP ⊆ NP/log if and only if EXP = P||NP.
Also known as Θ2P.
The class of decision problems solvable by a P machine, that can make O(log n) queries to an NP oracle (where n is the length of the input).
Equals P||NP, the class of decision problems solvable by a P machine that can make polynomially many nonadaptive queries to an NP oracle (i.e. queries that do not depend on the outcomes of previous queries) ([BH91] and [Hem89] independently).
PNP[log] is contained in PP [BHW89].
Determining the winner in an election system proposed in 1876 by Charles Dodgson (a.k.a. Lewis Carroll) has been shown to be complete for PNP[log] [HHR97].
Contains PNP[k] for all constants k.