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(1.025n).
An Exponential Lower Bound on OBDD Refutations for Pigeonhole Formulas
Proceedings of the 4th Athens Colloquium on Algorithms and Complexity
Electronic Proceedings in Theoretical Computer Science 4:13-21