An Exponential Lower Bound on OBDD Refutations for Pigeonhole Formulas
نویسندگان
چکیده
Haken proved that every resolution refutation of the pigeon hole formula has at least exponential size. Groote and Zantema proved that a particular OBDD computation of the pigeon hole formula has an exponential size. Here we show that any arbitrary OBDD refutation of the pigeon hole formula has an exponential size, too: we prove that the size of one of the intermediate OBDDs is at least Ω(1.025).
منابع مشابه
Ordered Binary Decision Diagrams, Pigeonhole Formulas and Beyond
Groote and Zantema proved that a particular OBDD computation of the pigeonhole formula has exponential size, and that limited OBDD derivations cannot simulate resolution polynomially. Here we show that an arbitrary OBDD refutation of the pigeonhole formula has exponential size: we prove that for any order of computation at least one intermediate OBDD in the proof has size Ω(1.14n). We also pres...
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