A model-theoretic characterization 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 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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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.
متن کاملResolution lower bounds for the weak functional pigeonhole principle
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.
متن کاملThe weak pigeonhole principle for function classes in S^1_2
It is well known that S1 2 cannot prove the injective weak pigeonhole principle for polynomial time functions unless RSA is insecure. In this note we investigate the provability of the surjective (dual) weak pigeonhole principle in S1 2 for provably weaker function classes. §
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ژورنال
عنوان ژورنال: Annals of Pure and Applied Logic
سال: 2002
ISSN: 0168-0072
DOI: 10.1016/s0168-0072(02)00038-6