An Exponential Lower Bound on OBDD Refutations for Pigeonhole Formulas

Details An Exponential Lower Bound on OBDD Refutations for Pigeonhole Formulas An Exponential Lower Bound on OBDD Refutations for Pigeonhole Formulas

2009-09-28

arxiv.org/abs/0909.5038v1

EPTCS 4, 2009, pp. 13-21

Computer Science

Computational Complexity

Scientific paper

10.4204/EPTCS.4.2

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 $\Omega(1.025^n)$.

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