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Cumulative Space in Black-White Pebbling and Resolution

Authors Joël Alwen, Susanna F. de Rezende, Jakob Nordström, Marc Vinyals

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Joël Alwen
Susanna F. de Rezende
Jakob Nordström
Marc Vinyals

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Joël Alwen, Susanna F. de Rezende, Jakob Nordström, and Marc Vinyals. Cumulative Space in Black-White Pebbling and Resolution. In 8th Innovations in Theoretical Computer Science Conference (ITCS 2017). Leibniz International Proceedings in Informatics (LIPIcs), Volume 67, pp. 38:1-38:21, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2017) https://doi.org/10.4230/LIPIcs.ITCS.2017.38

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.

Subject Classification

Keywords
  • pebble game
  • pebbling
  • proof complexity
  • space
  • cumulative space
  • clause space
  • resolution
  • parallel resolution

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