About: PSEUDO-FINITE HARD INSTANCES FOR A STUDENT-TEACHER GAME WITH A NISAN-WIGDERSON GENERATOR

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Attributes	Values
rdf:type	skos:Concept http://linked.opendata.cz/ontology/domain/vavai/Vysledek
rdfs:seeAlso	http://dx.doi.org/10.2168/LMCS-8(3:09)2012
Description	For an NP boolean AND coNP function g of the Nisan-Wigderson type and a string b outside its range we consider a two player game on a common input a to the function. One player, a computationally limited Student, tries to find a bit of g(a) that differs from the corresponding bit of b. He can query a computationally unlimited Teacher for the witnesses of the values of constantly many bits of g(a). The Student computes the queries from a and from Teacher's answers to his previous queries. It was proved in [Kra11b] that if g is based on a hard bit of a one-way permutation then no Student computed by a polynomial size circuit can succeed on all a. In this paper we give a lower bound on the number of inputs a any such Student must fail on. Using that we show that there is a pseudo-finite set of hard instances on which all uniform students must fail. The hard-core set is defined in a non-standard model of true arithmetic and has applications in a forcing construction from [Kra11a]. For an NP boolean AND coNP function g of the Nisan-Wigderson type and a string b outside its range we consider a two player game on a common input a to the function. One player, a computationally limited Student, tries to find a bit of g(a) that differs from the corresponding bit of b. He can query a computationally unlimited Teacher for the witnesses of the values of constantly many bits of g(a). The Student computes the queries from a and from Teacher's answers to his previous queries. It was proved in [Kra11b] that if g is based on a hard bit of a one-way permutation then no Student computed by a polynomial size circuit can succeed on all a. In this paper we give a lower bound on the number of inputs a any such Student must fail on. Using that we show that there is a pseudo-finite set of hard instances on which all uniform students must fail. The hard-core set is defined in a non-standard model of true arithmetic and has applications in a forcing construction from [Kra11a]. (en)
Title	PSEUDO-FINITE HARD INSTANCES FOR A STUDENT-TEACHER GAME WITH A NISAN-WIGDERSON GENERATOR PSEUDO-FINITE HARD INSTANCES FOR A STUDENT-TEACHER GAME WITH A NISAN-WIGDERSON GENERATOR (en)
skos:prefLabel	PSEUDO-FINITE HARD INSTANCES FOR A STUDENT-TEACHER GAME WITH A NISAN-WIGDERSON GENERATOR PSEUDO-FINITE HARD INSTANCES FOR A STUDENT-TEACHER GAME WITH A NISAN-WIGDERSON GENERATOR (en)
skos:notation	RIV/00216208:11320/12:10127159!RIV13-MSM-11320___
http://linked.open...avai/predkladatel	Matematicko-fyzikální fakulta
http://linked.open...avai/riv/aktivita	I P
http://linked.open...avai/riv/aktivity	I, P(IAA100190902)
http://linked.open...iv/cisloPeriodika	3
http://linked.open...vai/riv/dodaniDat	2013
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	Univerzita Karlova v Praze / Matematicko-fyzikální fakulta
http://linked.open...dnocenehoVysledku	163469
http://linked.open...ai/riv/idVysledku	RIV/00216208:11320/12:10127159
http://linked.open...riv/jazykVysledku	eng - angličtina
http://linked.open.../riv/klicovaSlova	GENERATOR; NISAN-WIGDERSON; WITH; GAME; STUDENT-TEACHER; FOR; INSTANCES; HARD; PSEUDO-FINITE (en)
http://linked.open.../riv/klicoveSlovo	FOR WITH GAME GENERATOR HARD INSTANCES NISAN-WIGDERSON PSEUDO-FINITE STUDENT-TEACHER
http://linked.open...odStatuVydavatele	DE - Spolková republika Německo
http://linked.open...ontrolniKodProRIV	[6EA98ACA8E82]
http://linked.open...i/riv/nazevZdroje	Logical Methods in Computer Science
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	Mathematical logic, complexity, and algorithms
http://linked.open...UplatneniVysledku	2012
http://linked.open...v/svazekPeriodika	8
http://linked.open...iv/tvurceVysledku	Krajíček, Jan
http://linked.open...ain/vavai/riv/wos	000309447200009
issn	1860-5974
number of pages	8 (xsd:int)
http://bibframe.org/vocab/doi	10.2168/LMCS-8(3:09)2012
http://localhost/t...ganizacniJednotka	11320
is http://linked.open...avai/riv/vysledek of	PSEUDO-FINITE HARD INSTANCES FOR A STUDENT-TEACHER GAME WITH A NISAN-WIGDERSON GENERATOR

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