The Complexity of Finding Top-Toda-Equivalence- Class Members

摘要

We identify two properties that for P-selective sets are effectively computable. Namely we show that, for any P-selective set, finding a string that is in a given length's top Toda equivalence class (very informally put, a string from Σ~n that the set's P-selector function declares to be most likely to belong to the set) is FP~(Σ_2~p) computable, and we show that each P-selective set contains a weakly-P~(Σ_2~p) -rankable subset.