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 Ω(1.025^{n}).

# An Exponential Lower Bound on OBDD Refutations for Pigeonhole Formulas

Author: | Olga Tveretina, Carsten Sinz, Hans Zantema |
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Source: | Proceedings of the 4th Athens Colloquium on Algorithms and Complexity Electronic Proceedings in Theoretical Computer Science 4:13-21 |
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Date: | 2009 | ||