Jan Krajíček - Pseudo-finite hard instances for a student-teacher game with a Nisan-Wigderson generator

lmcs:788 - Logical Methods in Computer Science, August 13, 2012, Volume 8, Issue 3 - https://doi.org/10.2168/LMCS-8(3:9)2012
Pseudo-finite hard instances for a student-teacher game with a Nisan-Wigderson generatorArticle

Authors: Jan Krajíček

    For an NP intersect 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 by Krajicek (2011) 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 relevant to proof complexity.


    Volume: Volume 8, Issue 3
    Published on: August 13, 2012
    Imported on: February 22, 2012
    Keywords: Computer Science - Computational Complexity,Mathematics - Logic,F.2.2,F.4.1

    27 Documents citing this article

    Consultation statistics

    This page has been seen 1474 times.
    This article's PDF has been downloaded 451 times.