On the Relative Strength of Pebbling and Resolution
2010 (English)In: Proceedings of the 25th Annual IEEE Conference on Computational Complexity (CCC '10), 2010, 151-162 p.Conference paper (Refereed)
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 find specific graph families which either have essentially the same properties for black and blackwhite pebbling (not at all true in general) or which admit simulations of black-white pebblings in resolution. This paper contributes to both these approaches. First, we design a restricted form of black-white pebbling that can be simulated in resolution and show that there are graph families for which such restricted pebblings can be asymptotically better than black pebblings. This proves that, perhaps somewhat unexpectedly, resolution can strictly beat black-only pebbling, and in particular that the space lower bounds on pebbling formulas in [Ben-Sasson and Nordstr¨om 2008] are tight. Second, we present a versatile parametrized graph family with essentially the same properties for black and black-white pebbling, which gives sharp simultaneous trade-offs for black and black-white pebbling for various parameter settings. Both of our contributions have been instrumental in obtaining the time-space trade-off results for resolution-based proof systems in [Ben-Sasson and Nordstr¨om 2009].
Place, publisher, year, edition, pages
2010. 151-162 p.
, Annual IEEE Conference on Computational Complexity, ISSN 1093-0159
complexity, resolution, pebble games, pebbling
Computer and Information Science
IdentifiersURN: urn:nbn:se:kth:diva-63091DOI: 10.1109/CCC.2010.22ISI: 000286932700015ISBN: 978-0-7695-4060-3OAI: oai:DiVA.org:kth-63091DiVA: diva2:481617
25th Annual IEEE Conference on Computational Complexity, Harward Univ, Cambridge, MA, JUN 09-11, 2010
QC 201202022012-01-212012-01-212012-02-02Bibliographically approved