About: A note on propositional proof complexity of some Ramsey-type statements

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rdf:type	skos:Concept http://linked.opendata.cz/ontology/domain/vavai/Vysledek
Description	A Ramsey statement denoted n -> (k)(2)(2) says that every undirected graph on n vertices contains either a clique or an independent set of size k. Any such valid statement can be encoded into a valid DNF formulaRAM(n, k) of size O(n(k)) and with terms of size ((k)(2)). Let r(k) be the minimal n for which the statement holds. We prove that RAM(r(k), k) requires exponential size constant depth Frege systems, answering a problem of Krishnamurthy and Moll [15]. As a consequence of Pudlak's work in bounded arithmetic [19] it is known that there are quasi-polynomial size constant depth Frege proofs of RAM(4(k), k), but the proof complexity of these formulas in resolution R or in its extension R(log) is unknown. We define two relativizations of the Ramsey statement that still have quasi-polynomial size constant depth Frege proofs but for which we establish exponential lower bound for R. A Ramsey statement denoted n -> (k)(2)(2) says that every undirected graph on n vertices contains either a clique or an independent set of size k. Any such valid statement can be encoded into a valid DNF formulaRAM(n, k) of size O(n(k)) and with terms of size ((k)(2)). Let r(k) be the minimal n for which the statement holds. We prove that RAM(r(k), k) requires exponential size constant depth Frege systems, answering a problem of Krishnamurthy and Moll [15]. As a consequence of Pudlak's work in bounded arithmetic [19] it is known that there are quasi-polynomial size constant depth Frege proofs of RAM(4(k), k), but the proof complexity of these formulas in resolution R or in its extension R(log) is unknown. We define two relativizations of the Ramsey statement that still have quasi-polynomial size constant depth Frege proofs but for which we establish exponential lower bound for R. (en)
Title	A note on propositional proof complexity of some Ramsey-type statements A note on propositional proof complexity of some Ramsey-type statements (en)
skos:prefLabel	A note on propositional proof complexity of some Ramsey-type statements A note on propositional proof complexity of some Ramsey-type statements (en)
skos:notation	RIV/67985840:_____/11:00369652!RIV12-AV0-67985840
http://linked.open...avai/predkladatel	Matematický ústav AV ČR, v. v. i.
http://linked.open...avai/riv/aktivita	P Z
http://linked.open...avai/riv/aktivity	P(IAA100190902), P(LC505), Z(AV0Z10190503), Z(MSM0021620839)
http://linked.open...iv/cisloPeriodika	1-2
http://linked.open...vai/riv/dodaniDat	2012
http://linked.open...aciTvurceVysledku	Krajíček, Jan
http://linked.open.../riv/druhVysledku	J - Článek v odborném periodiku
http://linked.open...iv/duvernostUdaju	S - Úplné a pravdivé údaje nepodléhající ochraně podle zvláštních právních předpisů
http://linked.open...titaPredkladatele	Matematický ústav AV ČR, v. v. i.
http://linked.open...dnocenehoVysledku	184001
http://linked.open...ai/riv/idVysledku	RIV/67985840:_____/11:00369652
http://linked.open...riv/jazykVysledku	eng - angličtina
http://linked.open.../riv/klicovaSlova	proof complexity; Ramsey theorem; resolution (en)
http://linked.open.../riv/klicoveSlovo	Ramsey theorem proof complexity resolution
http://linked.open...odStatuVydavatele	DE - Spolková republika Německo
http://linked.open...ontrolniKodProRIV	[9B6EFD0F55E3]
http://linked.open...i/riv/nazevZdroje	Archive for Mathematical Logic
http://linked.open...in/vavai/riv/obor	BA
http://linked.open...ichTvurcuVysledku	1 (xsd:int)
http://linked.open...cetTvurcuVysledku	1 (xsd:int)
http://linked.open...vavai/riv/projekt	Eduard Čech Center for Algebra and Geometry Mathematical logic, complexity, and algorithms
http://linked.open...UplatneniVysledku	2011
http://linked.open...v/svazekPeriodika	50
http://linked.open...iv/tvurceVysledku	Krajíček, Jan
http://linked.open...ain/vavai/riv/wos	000286668400014
http://linked.open...n/vavai/riv/zamer	Rozvoj a prohloubení obecných matematických poznatků a jejich užití v dalších vědních oborech a v praxi Metody moderní matematiky a jejich aplikace
issn	1432-0665
number of pages	11 (xsd:int)
http://bibframe.org/vocab/doi	10.1007/s00153-010-0212-9
is http://linked.open...avai/riv/vysledek of	A note on propositional proof complexity of some Ramsey-type statements A note on propositional proof complexity of some Ramsey-type statements

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