On minimal unsatisfiability and time-space trade-offs for k-DNF resolution

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

Abstract

A well-known theorem by Tarsi states that a minimally unsatisfiable CNF formula with m clauses can have at most m - 1 variables, and this bound is exact. In the context of proving lower bounds on proof space in k-DNF resolution, [Ben-Sasson and Nordström 2009] extended the concept of minimal unsatisfiability to sets of k-DNF formulas and proved that a minimally unsatisfiable k-DNF set with m formulas can have at most (mk) k + 1 variables. This result is far from tight, however, since they could only present explicit constructions of minimally unsatisfiable sets with Ω(mk 2) variables. In the current paper, we revisit this combinatorial problem and significantly improve the lower bound to (Ω(m)) k , which almost matches the upper bound above. Furthermore, using similar ideas we show that the analysis of the technique in [Ben-Sasson and Nordström 2009] for proving time-space separations and trade-offs for k-DNF resolution is almost tight. This means that although it is possible, or even plausible, that stronger results than in [Ben-Sasson and Nordström 2009] should hold, a fundamentally different approach would be needed to obtain such results.

Detaljer

Författare
Externa organisationer
  • KTH Royal Institute of Technology
  • University of Chicago
Forskningsområden

Ämnesklassifikation (UKÄ) – OBLIGATORISK

  • Datavetenskap (datalogi)
Originalspråkengelska
Titel på värdpublikationAutomata, Languages and Programming
Undertitel på gästpublikation38th International Colloquium, ICALP 2011, Proceedings
FörlagSpringer
Sidor642-653
Antal sidor12
UtgåvaPART 1
ISBN (tryckt)9783642220050
StatusPublished - 2011
PublikationskategoriForskning
Peer review utfördJa
Externt publiceradJa
Evenemang38th International Colloquium on Automata, Languages and Programming, ICALP 2011 - Zurich, Schweiz
Varaktighet: 2011 jul 42011 jul 8

Publikationsserier

NamnLecture Notes in Computer Science
FörlagSprnger
NummerPART 1
Volym6755
ISSN (tryckt)0302-9743
ISSN (elektroniskt)1611-3349

Konferens

Konferens38th International Colloquium on Automata, Languages and Programming, ICALP 2011
LandSchweiz
OrtZurich
Period2011/07/042011/07/08