Narrow proofs may be maximally long

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

Abstract

We prove that there are 3-CNF formulas over n variables that can be refuted in resolution in width w but require resolution proofs of size nω(w). This shows that the simple counting argument that any formula refutable in width w must have a proof in size nO(ω) is essentially tight. Moreover, our lower bounds can be generalized to polynomial calculus resolution (PCR) and Sherali-Adams, implying that the corresponding size upper bounds in terms of degree and rank are tight as well. Our results do not extend all the way to Lasserre, however-the formulas we study have Lasserre proofs of constant rank and size polynomial in both n and w.

Detaljer

Författare
Externa organisationer
  • Polytechnic University of Catalonia
  • KTH Royal Institute of Technology
Forskningsområden

Ämnesklassifikation (UKÄ) – OBLIGATORISK

  • Datavetenskap (datalogi)

Nyckelord

Originalspråkengelska
Titel på värdpublikationProceedings - IEEE 29th Conference on Computational Complexity, CCC 2014
FörlagIEEE - Institute of Electrical and Electronics Engineers Inc.
Sidor286-297
Antal sidor12
ISBN (tryckt)9781479936267
StatusPublished - 2014
PublikationskategoriForskning
Peer review utfördJa
Externt publiceradJa
Evenemang29th Annual IEEE Conference on Computational Complexity, CCC 2014 - Vancouver, BC, Kanada
Varaktighet: 2014 jun 112014 jun 13

Publikationsserier

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

Konferens

Konferens29th Annual IEEE Conference on Computational Complexity, CCC 2014
LandKanada
OrtVancouver, BC
Period2014/06/112014/06/13