Exponential lower bounds for the pigeonhole principle
نویسندگان
چکیده
منابع مشابه
Improved Resolution Lower Bounds for the Weak Pigeonhole Principle
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.
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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 and random unsatisfiable CNF formulas require exponential-size proofs in this system. This is the strongest system beyond Resolution for which such lower bounds are ...
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We show that every resolution proof of the functional version FPHPm n of the pigeonhole principle (in which one pigeon may not split between several holes) must have size exp ( Ω ( n (logm)2 )) . This implies an exp ( Ω(n1/3) ) bound when the number of pigeons m is arbitrary.
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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...
متن کامل$P \ne NP$, 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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ژورنال
عنوان ژورنال: Computational Complexity
سال: 1993
ISSN: 1016-3328,1420-8954
DOI: 10.1007/bf01200117