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Logic seminar

Resolution, Heavy Width and Pseudorandom Generators

Dmitry Sokolov
St Petersburg State University and PDMI RAS


Monday, 21. February 2022 - 16:00 to 17:30
Online - - contact before the meeting to join
Following the paper of Alekhnovich, Ben-Sasson, Razborov, Wigderson we call a pseudorandom generator hard for a propositional proof system P if P cannot efficiently prove the (properly encoded) statement that b is outside of the image for any string b \in {0, 1}^m.

In ABRW04 the authors suggested the "functional encoding" of the considered statement for Nisan--Wigderson generator that allows the introduction of "local" extension variables and gave a lower bound on the length of Resolution proofs if the number of extension variables is bounded by the n^2 (where n is the number of inputs of the PRG).

In this talk, we discuss a "heavy width" measure for Resolution that allows us to show a lower bound on the length of Resolution proofs of the considered statement for the Nisan--Wigderson generator with a superpolynomial number of local extension variables. It is a solution to one of the open problems from ABRW04.