On the Size of Classes with Weak Membership Properties

Abstract It is shown that the following classes have resource-bounded measure 0 in E: the class of P-selective sets, the class of P-multiselective sets, the class of cheatable sets, the class of easily countable sets, the class of easily approximable sets, the class of near-testable sets, the class of nearly near-testable sets, the class of locally self-reducible sets. These are corollaries of a more general result stating that the class of sets that are P-isomorphic to P-quasi-approximable sets has measure 0 in E. By considering the recent approach of Allender and Strauss for measuring in subexponential classes, we obtain similar results with respect to P for classes having weak logarithmic time membership properties.

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