On the relative strength of pebbling and resolution

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Abstract

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 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 Nordström 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 Nordström 2009].

Detaljer

Författare
Externa organisationer
  • Massachusetts Institute of Technology
Forskningsområden

Ämnesklassifikation (UKÄ) – OBLIGATORISK

  • Datavetenskap (datalogi)

Nyckelord

Originalspråkengelska
Titel på värdpublikationProceedings - 25th Annual IEEE Conference on Computational Complexity, CCC 2010
FörlagIEEE - Institute of Electrical and Electronics Engineers Inc.
Sidor151-162
Antal sidor12
ISBN (tryckt)9780769540603
StatusPublished - 2010
PublikationskategoriForskning
Peer review utfördJa
Externt publiceradJa
Evenemang25th Annual IEEE Conference on Computational Complexity, CCC 2010 - Cambridge, MA, USA
Varaktighet: 2010 jun 92010 jun 11

Publikationsserier

NamnProceedings of the Annual IEEE Conference on Computational Complexity
FörlagIEEE
ISSN (tryckt)1093-0159

Konferens

Konferens25th Annual IEEE Conference on Computational Complexity, CCC 2010
LandUSA
OrtCambridge, MA
Period2010/06/092010/06/11