Probabilistic type-2 operators and "almost"-classes

We define and examine several probabilistic operators ranging over sets (i. e., operators of type 2), among them the formerly studied ALMOST-operator. We compare their power and prove that they all coincide for a wide variety of classes. As a consequence, we characterize the ALMOST-operator which ran ges over infinite objects (sets) by a bounded-error probabilistic operator which ranges over strings, i.e., finite objects. This leads to a number of consequences about complexity classes of current interest. As applications, we obtain (a) a criterion for measure 1 inclusions of complexity classes, (b) a criterion for inclusions of complexity classes relative to a random o racle, (c) a new upper time bound for ALMOST-PSPACE, and (d) a characteriza tion of ALMOST-PSPACE in terms of checking stack automata. Finally, a conne ction between the power of ALMOST-PSPACE and that of probabilistic NC1 circ uits is given.