English

An Exponential Lower Bound on OBDD Refutations for Pigeonhole Formulas

Computational Complexity 2009-09-29 v1 Logic in Computer Science

Abstract

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)\Omega(1.025^n).

Cite

@article{arxiv.0909.5038,
  title  = {An Exponential Lower Bound on OBDD Refutations for Pigeonhole Formulas},
  author = {Olga Tveretina and Carsten Sinz and Hans Zantema},
  journal= {arXiv preprint arXiv:0909.5038},
  year   = {2009}
}
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