Improved bounds on the Weak Pigeonhole Principle and infinitely many primes from weaker axioms
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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We give new upper bounds for resolution proofs of the weak pigeonhole principle. We also give lower bounds for tree-like resolution proofs. We present a normal form for resolution proofs of pigeonhole principles based on a new monotone resolution rule.
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ژورنال
عنوان ژورنال: Theoretical Computer Science
سال: 2003
ISSN: 0304-3975
DOI: 10.1016/s0304-3975(02)00394-8