License: Creative Commons Attribution 4.0 International license (CC BY 4.0)
When quoting this document, please refer to the following
DOI: 10.4230/LIPIcs.ICALP.2022.73
URN: urn:nbn:de:0030-drops-164146
URL: http://dagstuhl.sunsite.rwth-aachen.de/volltexte/2022/16414/
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Holmgren, Justin ; Lincoln, Andrea ; Rothblum, Ron D.

Delegation for Search Problems

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LIPIcs-ICALP-2022-73.pdf (0.8 MB)

Abstract

The theory of proof systems in general, and interactive proofs in particular, has been immensely influential. Such proof systems allow a prover to convince a verifier whether a given statement is true or not - namely to solve a decision problem. In this work we initiate a study of interactive proofs for search problems.
More precisely, we consider a setting in which a client C, given an input x, would like to find a solution y satisfying (x,y) ∈ R, for a given relation R. The client wishes to delegate this work to an (untrusted) advisor A, who has more resources than C. We seek solutions in which the communication from A is short, and, in particular, shorter than the length of the output y. (In particular, this precludes the trivial solution of the advisor sending y and then proving that (x,y) ∈ R using a standard interactive proof.)
We show that such search delegation schemes exist for several problems of interest including (1) longest common subsequence (LCS) and edit distance, (2) parsing context-free grammars and (3) k-SAT.

BibTeX - Entry

@InProceedings{holmgren_et_al:LIPIcs.ICALP.2022.73,
  author =	{Holmgren, Justin and Lincoln, Andrea and Rothblum, Ron D.},
  title =	{{Delegation for Search Problems}},
  booktitle =	{49th International Colloquium on Automata, Languages, and Programming (ICALP 2022)},
  pages =	{73:1--73:18},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-235-8},
  ISSN =	{1868-8969},
  year =	{2022},
  volume =	{229},
  editor =	{Boja\'{n}czyk, Miko{\l}aj and Merelli, Emanuela and Woodruff, David P.},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/opus/volltexte/2022/16414},
  URN =		{urn:nbn:de:0030-drops-164146},
  doi =		{10.4230/LIPIcs.ICALP.2022.73},
  annote =	{Keywords: Interactive Proofs, Fine-Grained Complexity, Delegation}
}

Keywords: Interactive Proofs, Fine-Grained Complexity, Delegation
Collection: 49th International Colloquium on Automata, Languages, and Programming (ICALP 2022)
Issue Date: 2022
Date of publication: 28.06.2022

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