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Theory of Computing Systems

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

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

Article

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.

Keywords

Equivalence Class Binary Encode Reachability Problem Polynomial Hierarchy Mathematical System Theory 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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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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