Abstract
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 \({\rm FP}^{\Sigma^p_2}\) computable, and we show that each P-selective set contains a weakly-\(P^{\Sigma^p_2}\)-rankable subset.
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Hemaspaandra, L., Ogihara, M., Zaki, M. et al. The Complexity of Finding Top-Toda-Equivalence-Class Members. Theory Comput Syst 39, 669–684 (2006). https://doi.org/10.1007/s00224-005-1211-9
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DOI: https://doi.org/10.1007/s00224-005-1211-9