PSEUDO-FINITE HARD INSTANCES FOR A STUDENT-TEACHER GAME WITH A NISAN-WIGDERSON GENERATOR
The result's identifiers
Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216208%3A11320%2F12%3A10127159" target="_blank" >RIV/00216208:11320/12:10127159 - isvavai.cz</a>
Alternative codes found
RIV/67985840:_____/12:00385494
Result on the web
<a href="http://dx.doi.org/10.2168/LMCS-8(3:09)2012" target="_blank" >http://dx.doi.org/10.2168/LMCS-8(3:09)2012</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.2168/LMCS-8(3:09)2012" target="_blank" >10.2168/LMCS-8(3:09)2012</a>
Alternative languages
Result language
angličtina
Original language name
PSEUDO-FINITE HARD INSTANCES FOR A STUDENT-TEACHER GAME WITH A NISAN-WIGDERSON GENERATOR
Original language 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 differsfrom 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].
Czech name
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Czech description
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Classification
Type
J<sub>x</sub> - Unclassified - Peer-reviewed scientific article (Jimp, Jsc and Jost)
CEP classification
BA - General mathematics
OECD FORD branch
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Result continuities
Project
<a href="/en/project/IAA100190902" target="_blank" >IAA100190902: Mathematical logic, complexity, and algorithms</a><br>
Continuities
I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace
Others
Publication year
2012
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů
Data specific for result type
Name of the periodical
Logical Methods in Computer Science
ISSN
1860-5974
e-ISSN
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Volume of the periodical
8
Issue of the periodical within the volume
3
Country of publishing house
DE - GERMANY
Number of pages
8
Pages from-to
1-8
UT code for WoS article
000309447200009
EID of the result in the Scopus database
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