From small space to small width in resolution

Forskningsoutput: TidskriftsbidragArtikel i vetenskaplig tidskrift

Abstract

In 2003, Atserias and Dalmau resolved a major open question about the resolution proof system by establishing that the space complexity of a Conjunctive Normal Form (CNF) formula is always an upper bound on the width needed to refute the formula. Their proof is beautiful but uses a nonconstructive argument based on Ehrenfeucht-Fraïssé games. We give an alternative, more explicit, proof that works by simple syntactic manipulations of resolution refutations. As a by-product, we develop a "black-box" technique for proving space lower bounds via a "static" complexitymeasure that works against any resolution refutation-previous techniques have been inherently adaptive. We conclude by showing that the related question for polynomial calculus (i.e., whether space is an upper bound on degree) seems unlikely to be resolvable by similarmethods.

Detaljer

Författare
Externa organisationer
  • Institute for Advanced Study, Princeton
  • KTH Royal Institute of Technology
Forskningsområden

Ämnesklassifikation (UKÄ) – OBLIGATORISK

  • Beräkningsmatematik

Nyckelord

Originalspråkengelska
Artikelnummer28
TidskriftACM Transactions on Computational Logic
Volym16
Utgåva nummer4
StatusPublished - 2015 aug 1
PublikationskategoriForskning
Peer review utfördJa
Externt publiceradJa