Theory of Computing Systems

, Volume 39, Issue 5, pp 669–684 | Cite as

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 \({\rm FP}^{\Sigma^p_2}\) computable, and we show that each P-selective set contains a weakly-\(P^{\Sigma^p_2}\)-rankable subset.

Copyright information

© Springer 2005

Authors and Affiliations

  1. 1.Department of Computer Science, University of Rochester, Rochester, NY 14627USA
  2. 2.Department of Computer Science, Rensselaer Polytechnic Institute, Troy, NY 12180USA
  3. 3.Department of Computer and Information Sciences, Towson University, Towson, MD 21252USA

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