License: Creative Commons Attribution 3.0 Unported license (CC BY 3.0)
When quoting this document, please refer to the following
DOI: 10.4230/LIPIcs.ITCS.2020.57
URN: urn:nbn:de:0030-drops-117420
URL: http://dagstuhl.sunsite.rwth-aachen.de/volltexte/2020/11742/
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Chiesa, Alessandro ; Liu, Siqi

On the Impossibility of Probabilistic Proofs in Relativized Worlds

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LIPIcs-ITCS-2020-57.pdf (0.7 MB)

Abstract

We initiate the systematic study of probabilistic proofs in relativized worlds, where the goal is to understand, for a given oracle, the possibility of "non-trivial" proof systems for deterministic or nondeterministic computations that make queries to the oracle.
This question is intimately related to a recent line of work that seeks to improve the efficiency of probabilistic proofs for computations that use functionalities such as cryptographic hash functions and digital signatures, by instantiating them via constructions that are "friendly" to known constructions of probabilistic proofs. Informally, negative results about probabilistic proofs in relativized worlds provide evidence that this line of work is inherent and, conversely, positive results provide a way to bypass it.
We prove several impossibility results for probabilistic proofs relative to natural oracles. Our results provide strong evidence that tailoring certain natural functionalities to known probabilistic proofs is inherent.

BibTeX - Entry

@InProceedings{chiesa_et_al:LIPIcs:2020:11742,
  author =	{Alessandro Chiesa and Siqi Liu},
  title =	{{On the Impossibility of Probabilistic Proofs in Relativized Worlds}},
  booktitle =	{11th Innovations in Theoretical Computer Science Conference (ITCS 2020)},
  pages =	{57:1--57:30},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-134-4},
  ISSN =	{1868-8969},
  year =	{2020},
  volume =	{151},
  editor =	{Thomas Vidick},
  publisher =	{Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/opus/volltexte/2020/11742},
  URN =		{urn:nbn:de:0030-drops-117420},
  doi =		{10.4230/LIPIcs.ITCS.2020.57},
  annote =	{Keywords: probabilistically checkable proofs, relativization}
}

Keywords: probabilistically checkable proofs, relativization
Collection: 11th Innovations in Theoretical Computer Science Conference (ITCS 2020)
Issue Date: 2020
Date of publication: 06.01.2020

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