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.2017.38
URN: urn:nbn:de:0030-drops-81918
URL: http://dagstuhl.sunsite.rwth-aachen.de/volltexte/2017/8191/
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Alwen, Joël ; de Rezende, Susanna F. ; Nordström, Jakob ; Vinyals, Marc

Cumulative Space in Black-White Pebbling and Resolution

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LIPIcs-ITCS-2017-38.pdf (0.5 MB)

Abstract

We study space complexity and time-space trade-offs with a focus not on peak memory usage but on overall memory consumption throughout the computation. Such a cumulative space measure was introduced for the computational model of parallel black pebbling by [Alwen and Serbinenko 2015] as a tool for obtaining results in cryptography. We consider instead the nondeterministic black-white pebble game and prove optimal cumulative space lower bounds and trade-offs, where in order to minimize pebbling time the space has to remain large during a significant fraction of the pebbling.

We also initiate the study of cumulative space in proof complexity, an area where other space complexity measures have been extensively studied during the last 10-15 years. Using and extending the connection between proof complexity and pebble games in [Ben-Sasson and Nordström 2008, 2011], we obtain several strong cumulative space results for (even parallel versions of) the resolution proof system, and outline some possible future directions of study of this, in our opinion, natural and interesting space measure.

BibTeX - Entry

@InProceedings{alwen_et_al:LIPIcs:2017:8191,
  author =	{Jo{\"e}l Alwen and Susanna F. de Rezende and Jakob Nordstr{\"o}m and Marc Vinyals},
  title =	{{Cumulative Space in Black-White Pebbling and Resolution}},
  booktitle =	{8th Innovations in Theoretical Computer Science Conference (ITCS 2017)},
  pages =	{38:1--38:21},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-029-3},
  ISSN =	{1868-8969},
  year =	{2017},
  volume =	{67},
  editor =	{Christos H. Papadimitriou},
  publisher =	{Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{http://drops.dagstuhl.de/opus/volltexte/2017/8191},
  URN =		{urn:nbn:de:0030-drops-81918},
  doi =		{10.4230/LIPIcs.ITCS.2017.38},
  annote =	{Keywords: pebble game, pebbling, proof complexity, space, cumulative space, clause space, resolution, parallel resolution}
}

Keywords: pebble game, pebbling, proof complexity, space, cumulative space, clause space, resolution, parallel resolution
Collection: 8th Innovations in Theoretical Computer Science Conference (ITCS 2017)
Issue Date: 2017
Date of publication: 28.11.2017

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