Narrow proofs may be maximally long

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Abstract

We prove that there are 3-conjunctive normal form 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(w) is essentially tight. Moreover, our lower bound generalizes to polynomial calculus resolution and Sherali-Adams, implying that the corresponding size upper bounds in terms of degree and rank are tight as well. The lower bound does not extend all the way to Lasserre, however, since we show that there the formulas we study have proofs of constant rank and size polynomial in both n and w.

Detaljer

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

Ämnesklassifikation (UKÄ) – OBLIGATORISK

  • Beräkningsmatematik

Nyckelord

Originalspråkengelska
Artikelnummer19
TidskriftACM Transactions on Computational Logic
Volym17
Utgåva nummer3
StatusPublished - 2016 feb
PublikationskategoriForskning
Peer review utfördJa
Externt publiceradJa