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On the Relative Strength of Pebbling and Resolution

On the Relative Strength of Pebbling and Resolution On the Relative Strength of Pebbling and Resolution JAKOB NORDSTROM, KTH Royal Institute of Technology The last decade has seen a revival of interest in pebble games in the context of proof complexity. Pebbling has proven to be a useful tool for studying resolution-based proof systems when comparing the strength of different subsystems, showing bounds on proof space, and establishing size-space trade-offs. The typical approach has been to encode the pebble game played on a graph as a CNF formula and then argue that proofs of this formula must inherit (various aspects of) the pebbling properties of the underlying graph. Unfortunately, the reductions used here are not tight. To simulate resolution proofs by pebblings, the full strength of nondeterministic black-white pebbling is needed, whereas resolution is only known to be able to simulate deterministic black pebbling. To obtain strong results, one therefore needs to nd speci c graph families which either have essentially the same properties for black and black-white pebbling (not at all true in general) or which admit simulations of black-white pebblings in resolution. This article contributes to both these approaches. First, we design a restricted form of black-white pebbling that can be simulated in resolution http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png ACM Transactions on Computational Logic (TOCL) Association for Computing Machinery

On the Relative Strength of Pebbling and Resolution

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Publisher
Association for Computing Machinery
Copyright
Copyright © 2012 by ACM Inc.
ISSN
1529-3785
DOI
10.1145/2159531.2159538
Publisher site
See Article on Publisher Site

Abstract

On the Relative Strength of Pebbling and Resolution JAKOB NORDSTROM, KTH Royal Institute of Technology The last decade has seen a revival of interest in pebble games in the context of proof complexity. Pebbling has proven to be a useful tool for studying resolution-based proof systems when comparing the strength of different subsystems, showing bounds on proof space, and establishing size-space trade-offs. The typical approach has been to encode the pebble game played on a graph as a CNF formula and then argue that proofs of this formula must inherit (various aspects of) the pebbling properties of the underlying graph. Unfortunately, the reductions used here are not tight. To simulate resolution proofs by pebblings, the full strength of nondeterministic black-white pebbling is needed, whereas resolution is only known to be able to simulate deterministic black pebbling. To obtain strong results, one therefore needs to nd speci c graph families which either have essentially the same properties for black and black-white pebbling (not at all true in general) or which admit simulations of black-white pebblings in resolution. This article contributes to both these approaches. First, we design a restricted form of black-white pebbling that can be simulated in resolution

Journal

ACM Transactions on Computational Logic (TOCL)Association for Computing Machinery

Published: Apr 1, 2012

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