Schloss Dagstuhl - Leibniz-Zentrum für Informatik GmbH Schloss Dagstuhl - Leibniz-Zentrum für Informatik GmbH scholarly article en Goldwasser, Shafi; Impagliazzo, Russell; Pitassi, Toniann; Santhanam, Rahul https://www.dagstuhl.de/lipics License: Creative Commons Attribution 4.0 license (CC BY 4.0)
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URN: urn:nbn:de:0030-drops-143104
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On the Pseudo-Deterministic Query Complexity of NP Search Problems

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Abstract

We study pseudo-deterministic query complexity - randomized query algorithms that are required to output the same answer with high probability on all inputs. We prove Ω(√n) lower bounds on the pseudo-deterministic complexity of a large family of search problems based on unsatisfiable random CNF instances, and also for the promise problem (FIND1) of finding a 1 in a vector populated with at least half one’s. This gives an exponential separation between randomized query complexity and pseudo-deterministic complexity, which is tight in the quantum setting. As applications we partially solve a related combinatorial coloring problem, and we separate random tree-like Resolution from its pseudo-deterministic version. In contrast to our lower bound, we show, surprisingly, that in the zero-error, average case setting, the three notions (deterministic, randomized, pseudo-deterministic) collapse.

BibTeX - Entry

@InProceedings{goldwasser_et_al:LIPIcs.CCC.2021.36,
  author =	{Goldwasser, Shafi and Impagliazzo, Russell and Pitassi, Toniann and Santhanam, Rahul},
  title =	{{On the Pseudo-Deterministic Query Complexity of NP Search Problems}},
  booktitle =	{36th Computational Complexity Conference (CCC 2021)},
  pages =	{36:1--36:22},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-193-1},
  ISSN =	{1868-8969},
  year =	{2021},
  volume =	{200},
  editor =	{Kabanets, Valentine},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/opus/volltexte/2021/14310},
  URN =		{urn:nbn:de:0030-drops-143104},
  doi =		{10.4230/LIPIcs.CCC.2021.36},
  annote =	{Keywords: Pseudo-determinism, Query complexity, Proof complexity}
}

Keywords: Pseudo-determinism, Query complexity, Proof complexity
Seminar: 36th Computational Complexity Conference (CCC 2021)
Issue date: 2021
Date of publication: 08.07.2021


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