Amplification with One NP Oracle Query

Author Thomas Watson

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Author Details

Thomas Watson
  • University of Memphis, Memphis, TN, USA

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Thomas Watson. Amplification with One NP Oracle Query. In 46th International Colloquium on Automata, Languages, and Programming (ICALP 2019). Leibniz International Proceedings in Informatics (LIPIcs), Volume 132, pp. 96:1-96:13, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2019)


We provide a complete picture of the extent to which amplification of success probability is possible for randomized algorithms having access to one NP oracle query, in the settings of two-sided, one-sided, and zero-sided error. We generalize this picture to amplifying one-query algorithms with q-query algorithms, and we show our inclusions are tight for relativizing techniques.

Subject Classification

ACM Subject Classification
  • Theory of computation → Computational complexity and cryptography
  • Amplification
  • NP
  • oracle
  • query


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  1. Richard Beigel. Bounded Queries to SAT and the Boolean Hierarchy. Theoretical Computer Science, 84(2):199-223, 1991. URL:
  2. Jin-Yi Cai and Venkatesan Chakaravarthy. On Zero Error Algorithms Having Oracle Access to One Query. Journal of Combinatorial Optimization, 11(2):189-202, 2006. URL:
  3. Richard Chang and Suresh Purini. Amplifying ZPP^SAT[1] and the Two Queries Problem. In Proceedings of the 23rd Conference on Computational Complexity (CCC), pages 41-52. IEEE, 2008. URL:
  4. Rahul Tripathi. The 1-Versus-2 Queries Problem Revisited. Theory of Computing Systems, 46(2):193-221, 2010. URL:
  5. Nikolai Vereshchagin. Relativizability in Complexity Theory. In Provability, Complexity, Grammars, volume 192 of AMS Translations, Series 2, pages 87-172. American Mathematical Society, 1999. Google Scholar
  6. Thomas Watson. Amplification with One NP Oracle Query. Technical Report TR18-058, Electronic Colloquium on Computational Complexity (ECCC), 2018. URL:
  7. Thomas Watson. A ZPP^NP[1] Lifting Theorem. In Proceedings of the 36th International Symposium on Theoretical Aspects of Computer Science (STACS), pages 59:1-59:16. Schloss Dagstuhl, 2019. URL:
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