A New Proof of the Weak Pigeonhole Principle
نویسندگان
چکیده
منابع مشابه
Resolution and the Weak Pigeonhole Principle
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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The schematic CERES method is a method of cut elimination for proof schemata, that is a sequence of proofs with a recursive construction. Proof schemata can be thought of as a way to circumvent the addition of an induction rule to the LK-calculus. In this work, we formalize a schematic version of the Infinitary Pigeonhole Principle (IPP), in the LKS-calculus [9], and analyse the extracted claus...
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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 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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The principle sPHPb (PV (α)) states that no oracle circuit can compute a surjection of a onto b. We show that sPHP P (a)(PV (α)) is independent of PV1(α)+ sPHP π(a) Π(a)(PV (α)) for various choices of the parameters π, Π, %, P . We also improve the known separation of iWPHP(PV ) from S 2 + sWPHP(PV ) under cryptographic assumptions.
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ژورنال
عنوان ژورنال: Journal of Computer and System Sciences
سال: 2002
ISSN: 0022-0000
DOI: 10.1006/jcss.2002.1830