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AN INDUCTION PRINCIPLE AND PIGEONHOLE PRINCIPLES FOR KFINITE SETS
, 1994
"... Abstract. We establish a courseofvalues induction principle for Kfinite sets in intuitionistic type theory. Using this principle, we prove a pigeonhole principle conjectured by Bénabou and Loiseau. We also comment on some variants of this pigeonhole principle. 1. ..."
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Abstract. We establish a courseofvalues induction principle for Kfinite sets in intuitionistic type theory. Using this principle, we prove a pigeonhole principle conjectured by Bénabou and Loiseau. We also comment on some variants of this pigeonhole principle. 1.
Circuit Principles and Weak Pigeonhole Variants
, 2005
"... This paper considers the relational versions of the surjective and multifunction weak pigeonhole principles for PV , # 1 and # 2 formulas. We show that the relational surjective pigeonhole principle for # 2 formulas 2 implies a circuit blockrecognition principle which in turn implies the ..."
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This paper considers the relational versions of the surjective and multifunction weak pigeonhole principles for PV , # 1 and # 2 formulas. We show that the relational surjective pigeonhole principle for # 2 formulas 2 implies a circuit blockrecognition principle which in turn implies
On independence of variants of the weak pigeonhole principle
, 2007
"... The principle sPHP a b (P V (α)) states that no oracle circuit can compute a surjection of a onto b. We show that sPHP ϱ(a) π(a) P (a) (P V (α)) is independent of P V1(α)+sPHP Π(a) (P V (α)) for various choices of the parameters π, Π, ϱ, P. We also improve the known separation of iWPHP(P V) from S 1 ..."
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Cited by 3 (1 self)
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The principle sPHP a b (P V (α)) states that no oracle circuit can compute a surjection of a onto b. We show that sPHP ϱ(a) π(a) P (a) (P V (α)) is independent of P V1(α)+sPHP Π(a) (P V (α)) for various choices of the parameters π, Π, ϱ, P. We also improve the known separation of iWPHP(P V) from
Matrix identities and the pigeonhole principle
 ARCH MATH LOGIC
, 2004
"... We show that short boundeddepth Frege proofs of matrix identities, such as PQ I (over the field of two elements), imply short boundeddepth Frege proofs of the pigeonhole principle. Since the latter principle is known to require exponential size boundeddepth Frege proofs, it follows that t ..."
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Cited by 2 (1 self)
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We show that short boundeddepth Frege proofs of matrix identities, such as PQ I (over the field of two elements), imply short boundeddepth Frege proofs of the pigeonhole principle. Since the latter principle is known to require exponential size boundeddepth Frege proofs, it follows
On Tao’s “finitary” infinite pigeonhole principle
 The Journal of Symbolic Logic
, 2010
"... In 2007, Terence Tao wrote on his blog an essay about soft analysis, hard analysis and the finitization of soft analysis statements into hard analysis statements. One of his main examples was a quasifinitization of the infinite pigeonhole principle IPP, arriving at the “finitary ” infinite pigeonho ..."
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Cited by 6 (2 self)
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In 2007, Terence Tao wrote on his blog an essay about soft analysis, hard analysis and the finitization of soft analysis statements into hard analysis statements. One of his main examples was a quasifinitization of the infinite pigeonhole principle IPP, arriving at the “finitary ” infinite
Exploring the Computational Content of the Infinite Pigeonhole Principle
 the Journal of Logic and Computation
"... The use of classical logic for some combinatorial proofs, as it is the case with Ramsey’s theorem, can be localized in the Infinite Pigeonhole (IPH) principle, stating that any infinite sequence which is finitely colored has an infinite monochromatic subsequence. Since in general there is no comput ..."
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Cited by 5 (0 self)
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The use of classical logic for some combinatorial proofs, as it is the case with Ramsey’s theorem, can be localized in the Infinite Pigeonhole (IPH) principle, stating that any infinite sequence which is finitely colored has an infinite monochromatic subsequence. Since in general there is no com
TreeResolution complexity of the Weak PigeonHole Principle
"... We show some tight results about the treeresolution complexity of the Weak PigeonHole Principle, PHPmn. We prove that any optimal treeresolution proof of PHPmn is of size 2θ n logn , independently from m, even if it is infinity. So far, the lower bound know has been 2Ω n . We also show that an ..."
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We show some tight results about the treeresolution complexity of the Weak PigeonHole Principle, PHPmn. We prove that any optimal treeresolution proof of PHPmn is of size 2θ n logn , independently from m, even if it is infinity. So far, the lower bound know has been 2Ω n . We also show
Dual weak pigeonhole principle, Boolean complexity, and derandomization
, 2003
"... We study the extension (introduced as BT in [5]) of the theory S 1 2 by instances of the dual (onto) weak pigeonhole principle for ptime functions, dWPHP(PV) x x 2. We propose a natural framework for formalization of randomized algorithms in bounded arithmetic, and use it to provide a strengthening ..."
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We study the extension (introduced as BT in [5]) of the theory S 1 2 by instances of the dual (onto) weak pigeonhole principle for ptime functions, dWPHP(PV) x x 2. We propose a natural framework for formalization of randomized algorithms in bounded arithmetic, and use it to provide a
An Exponential Separation between the Matching Principle and the Pigeonhole Principle
 IN 8TH ANNUAL IEEE SYMPOSIUM ON LOGIC IN COMPUTER SCIENCE
, 1993
"... The combinatorial matching principle states that there is no perfect matching on an odd number of vertices. This principle generalizes the pigeonhole principle, which states that for a fixed bipartition of the vertices, there is no perfect matching between them. Therefore, it follows from recent lo ..."
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Cited by 16 (5 self)
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The combinatorial matching principle states that there is no perfect matching on an odd number of vertices. This principle generalizes the pigeonhole principle, which states that for a fixed bipartition of the vertices, there is no perfect matching between them. Therefore, it follows from recent
An Exponential Separation between the Parity Principle and the Pigeonhole Principle
 Annals of Pure and Applied Logic
, 1996
"... The combinatorial parity principle states that there is no perfect matching on an odd number of vertices. This principle generalizes the pigeonhole principle, which states that for a fixed bipartition of the vertices, there is no perfect matching between them. Therefore, it follows from recent lowe ..."
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Cited by 9 (0 self)
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The combinatorial parity principle states that there is no perfect matching on an odd number of vertices. This principle generalizes the pigeonhole principle, which states that for a fixed bipartition of the vertices, there is no perfect matching between them. Therefore, it follows from recent
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