An Exponential Lower Bound on OBDD Refutations for Pigeonhole Formulas

Haken proved that every resolution refutation of the pigeonhole formula has at least exponential size. Groote and Zantema proved that a particular OBDD computation of the pigeonhole formula has an exponential size. Here we show that any arbitrary OBDD refutation of the pigeonhole formula has an expo...

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Veröffentlicht in:Electronic proceedings in theoretical computer science 2009-09, Vol.4 (Proc. ACAC 2009), p.13-21
Hauptverfasser: Tveretina, Olga, Sinz, Carsten, Zantema, Hans
Format: Artikel
Sprache:eng
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Zusammenfassung:Haken proved that every resolution refutation of the pigeonhole formula has at least exponential size. Groote and Zantema proved that a particular OBDD computation of the pigeonhole formula has an exponential size. Here we show that any arbitrary OBDD refutation of the pigeonhole formula has an exponential size, too: we prove that the size of one of the intermediate OBDDs is at least $Omega(1.025^n)$.
ISSN:2075-2180
2075-2180
DOI:10.4204/EPTCS.4.2