The class of decision problems solvable by an NP machine such that the number of accepting paths exactly equals the number of rejecting paths, if and only if the answer is 'yes.'
The class of decision problems solvable by an NP machine such that
(Here all computation paths have the same length.)
Defined in [Wat15], where it was shown that BC=P admits efficient amplification and is closed under union, intersection, disjunction, and conjunction, and that coRP ⊆ BC=P ⊆ BPP.
Has the same relation to L as C=P does to P.
C=LC=L = LC=L [ABO99].
The class of decision problems solvable by an NP machine such that
Contained in C=P, and in ModkP for any odd k. Contains UP.
Defined in [BHR00].
The class of decision problems solvable by an NP machine such that
Defined in [FFK94], where it was also shown that LWPP is low for PP and C=P. (I.e. adding LWPP as an oracle does not increase the power of these classes.)
Contains SPP.
Also, contains the graph isomorphism problem [KST92].
Contains a whole litter of problems for solvable black-box groups: group intersection, group factorization, coset intersection, and double-coset membership [Vin04].
The class of decision problems solvable by an NP machine such that
We may additionally require that all paths make the same number of binary nondeterministic choices, but then the second condition has to be modified so that if the answer is "yes", the number of accepting and rejecting paths differ by 2. (If the total number of paths is even then the numbers can't differ by 1.)
Defined in [FFK94], where it was also shown that SPP is low for PP, C=P, ModkP, and SPP itself. (I.e. adding SPP as an oracle does not increase the power of these classes.)
Independently defined in [OH93], who called the class XP.
Contained in LWPP, C=P, and WPP among other classes.
Contains FewP; indeed, FewP is low for SPP, so that SPPFewP = SPP [FFK94].
Contains the problem of deciding whether a graph has any nontrivial automorphisms [KST92].
Indeed, contains graph isomorphism [AK02].
Contains a whole gaggle of problems for solvable black-box groups: solvability testing, membership testing, subgroup testing, normality testing, order verification, nilpotetence testing, group isomorphism, and group intersection [Vin04]
[AK02] also showed that the Hidden Subgroup Problem for permutation groups, of interest in quantum computing, is in FPSPP.
The class of decision problems solvable by an NP machine such that
Defined in [FFK94].
Contained in C=P ∩ coC=P, as well as AWPP.