Short proofs may be spacious: An optimal separation of space and length in resolution

Forskningsoutput: Kapitel i bok/rapport/Conference proceedingKonferenspaper i proceeding

Abstract

A number of works have looked at the relationship between length and space of resolution proofs. A notorious question has been whether the existence of a short proof implies the existence of a proof that can be verified using limited space. In this paper we resolve the question by answering it negatively in the strongest possible way. We show that there are families of 6-CNF formulas of size n, for arbitrarily large n, that have resolution proofs of length O(n) but for which any proof requires space Ω(n/log n). This is the strongest asymptotic separation possible since any proof of length O(n) can always be transformed into a proof in space O(n/log n). Our result follows by reducing the space complexity of so called pebbling formulas over a directed acyclic graph to the black-white pebbling price of the graph. The proof is somewhat simpler than previous results (in particular, those reported in [Nordström 2006, Nordström and Håstad 2008]) as it uses a slightly different flavor of pebbling formulas which allows for a rather straightforward reduction of proof space to standard black-white pebbling price.

Detaljer

Författare
Externa organisationer
  • Technion - Israel Institute of Technology
  • KTH Royal Institute of Technology
Forskningsområden

Ämnesklassifikation (UKÄ) – OBLIGATORISK

  • Datavetenskap (datalogi)
Originalspråkengelska
Titel på värdpublikationProceedings of the 49th Annual IEEE Symposium on Foundations of Computer Science, FOCS 2008
FörlagIEEE - Institute of Electrical and Electronics Engineers Inc.
Sidor709-718
Antal sidor10
ISBN (tryckt)9780769534367
StatusPublished - 2008
PublikationskategoriForskning
Peer review utfördJa
Externt publiceradJa
Evenemang49th Annual IEEE Symposium on Foundations of Computer Science, FOCS 2008 - Philadelphia, PA, USA
Varaktighet: 2008 okt 252008 okt 28

Publikationsserier

NamnProceedings - Annual IEEE Symposium on Foundations of Computer Science, FOCS
FörlagIEEE
ISSN (tryckt)0272-5428

Konferens

Konferens49th Annual IEEE Symposium on Foundations of Computer Science, FOCS 2008
LandUSA
OrtPhiladelphia, PA
Period2008/10/252008/10/28