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.ITCS.2023.67
URN: urn:nbn:de:0030-drops-175700
URL: http://dagstuhl.sunsite.rwth-aachen.de/volltexte/2023/17570/
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Harsha, Prahladh ; Mitropolsky, Daniel ; Rosen, Alon

Downward Self-Reducibility in TFNP

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LIPIcs-ITCS-2023-67.pdf (2 MB)

Abstract

A problem is downward self-reducible if it can be solved efficiently given an oracle that returns solutions for strictly smaller instances. In the decisional landscape, downward self-reducibility is well studied and it is known that all downward self-reducible problems are in PSPACE. In this paper, we initiate the study of downward self-reducible search problems which are guaranteed to have a solution - that is, the downward self-reducible problems in TFNP. We show that most natural PLS-complete problems are downward self-reducible and any downward self-reducible problem in TFNP is contained in PLS. Furthermore, if the downward self-reducible problem is in TFUP (i.e. it has a unique solution), then it is actually contained in UEOPL, a subclass of CLS. This implies that if integer factoring is downward self-reducible then it is in fact in UEOPL, suggesting that no efficient factoring algorithm exists using the factorization of smaller numbers.

BibTeX - Entry

@InProceedings{harsha_et_al:LIPIcs.ITCS.2023.67,
  author =	{Harsha, Prahladh and Mitropolsky, Daniel and Rosen, Alon},
  title =	{{Downward Self-Reducibility in TFNP}},
  booktitle =	{14th Innovations in Theoretical Computer Science Conference (ITCS 2023)},
  pages =	{67:1--67:17},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-263-1},
  ISSN =	{1868-8969},
  year =	{2023},
  volume =	{251},
  editor =	{Tauman Kalai, Yael},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/opus/volltexte/2023/17570},
  URN =		{urn:nbn:de:0030-drops-175700},
  doi =		{10.4230/LIPIcs.ITCS.2023.67},
  annote =	{Keywords: downward self-reducibility, TFNP, TFUP, factoring, PLS, CLS}
}

Keywords: downward self-reducibility, TFNP, TFUP, factoring, PLS, CLS
Collection: 14th Innovations in Theoretical Computer Science Conference (ITCS 2023)
Issue Date: 2023
Date of publication: 01.02.2023

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