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

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 Sigma^n that the set's P-selector function declares to be most likely to belong to the set) is FP^{Sigma_2^p} computable, and we show that each P-selective set contains a weakly-P^{Sigma_2^p}$-rankable subset