Improved Resolution Lower Bounds for the Weak Pigeonhole Principle
نویسنده
چکیده
Recently, Raz Raz01] established exponential lower bounds on the size of resolution proofs of the weak pigeonhole principle. We give another proof of this result which leads to better numerical bounds.
منابع مشابه
$P \ne NP$, propositional proof complexity, and resolution lower bounds for the weak pigeonhole principle
Recent results established exponential lower bounds for the length of any Resolution proof for the weak pigeonhole principle. More formally, it was proved that any Resolution proof for the weak pigeonhole principle, with n holes and any number of pigeons, is of length Ω(2n ǫ ), (for a constant ǫ = 1/3). One corollary is that certain propositional formulations of the statement P 6= NP do not hav...
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Recent results established exponential lower bounds for the length of any Resolution proof for the weak pigeonhole principle. More formally, it was proved that any Resolution proof for the weak pigeonhole principle, with n holes and any number of pigeons, is of length fl(2 ), (for a constant e = 1/3). One corollary is that certain propositional formulations of the statement P / NP do not have s...
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We work with an extension of Resolution, called Res(2), that allows clauses with conjunctions of two literals. In this system there are rules to introduce and eliminate such conjunctions. We prove that the weak pigeonhole principle PHPcn n and random unsatisfiable CNF formulas require exponential-size proofs in this system. This is the strongest system beyond Resolution for which such lower bou...
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We give simple new lower bounds on the lengths of Resolution proofs for the pigeonhole principle and for randomly generated formulas. For random formulas, our bounds signiicantly extend the range of formula sizes for which non-trivial lower bounds are known. For example, we show that with probability approaching 1, any Resolution refutation of a randomly chosen 3-CNF formula with at most n 6=5?...
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ورودعنوان ژورنال:
- Electronic Colloquium on Computational Complexity (ECCC)
دوره 8 شماره
صفحات -
تاریخ انتشار 2001