Computer Science – Computational Complexity
Scientific paper
2010-03-15
Computer Science
Computational Complexity
Full-length version of paper to appear in Proceedings of the 25th Annual IEEE Conference on Computational Complexity (CCC '10)
Scientific paper
The last decade has seen a revival of interest in pebble games in the context of proof complexity. Pebbling has proven 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 black-white 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 Nordstrom 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 Nordstrom 2009].
No associations
LandOfFree
On the Relative Strength of Pebbling and Resolution does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.
If you have personal experience with On the Relative Strength of Pebbling and Resolution, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and On the Relative Strength of Pebbling and Resolution will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-244662