The class of problems decidable by an O(f(n))-space Turing machine with two kinds of quantifiers: existential and randomized.
Contains NSPACE(f(n)) and BPSPACE(f(n)), and is contained in AUC-SPACE(f(n)).
By linear programming, GAN-SPACE(log n) is contained in P.
The class of problems decidable by an O(f(n))-space Turing machine with three kinds of quantifiers: existential, universal, and randomized.
Contains GAN-SPACE(f(n)).
AUC-SPACE(poly(n)) = SAPTIME = PSPACE [Pap83].
[Con92] shows that AUC-SPACE(log n) has a natural complete problem, and is contained in NP ∩ coNP.