Circuit principles and weak pigeonhole variants
نویسندگان
چکیده
منابع مشابه
Circuit Principles and Weak Pigeonhole Variants
This paper considers the relational versions of the surjective and multifunction weak pigeonhole principles for PV , Σ1 and Θ b 2-formulas. We show that the relational surjective pigeonhole principle for Θ2 formulas in S 1 2 implies a circuit block-recognition principle which in turn implies the surjective weak pigeonhole principle for Σ1 formulas. We introduce a class of predicates correspondi...
متن کاملCircuit principles and weak pigeonhole variants 1
This paper considers the relational versions of the surjective, partial surjective, and multifunction weak pigeonhole principles for PV , Σ1, Π b 1, and B(Σ b 1)-formulas as well as relativizations of these formulas to higher levels of the bounded arithmetic hierarchy. We show that the partial surjective weak pigeonhole principle for Π1 formulas implies that for each k there is a string of leng...
متن کاملOn Independence of Variants of the Weak Pigeonhole Principle
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.
متن کاملProof Complexity of Pigeonhole Principles
The pigeonhole principle asserts that there is no injective mapping from m pigeons to n holes as long as m > n. It is amazingly simple, expresses one of the most basic primitives in mathematics and Theoretical Computer Science (counting) and, for these reasons, is probably the most extensively studied combinatorial principle. In this survey we try to summarize what is known about its proof comp...
متن کاملResolution 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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ژورنال
عنوان ژورنال: Theoretical Computer Science
سال: 2007
ISSN: 0304-3975
DOI: 10.1016/j.tcs.2007.04.017