Pseudo-mixing time of random walks

Research output: Chapter in Book/Report/Conference proceedingChapter

Abstract

We introduce the notion of pseudo-mixing time of a graph, defined as the number of steps in a random walk that suffices for generating a vertex that looks random to any polynomial-time observer. Here, in addition to the tested vertex, the observer is also provided with oracle access to the incidence function of the graph. Assuming the existence of one-way functions, we show that the pseudo-mixing time of a graph can be much smaller than its mixing time. Specifically, we present bounded-degree N-vertex Cayley graphs that have pseudo-mixing time t for any t(N)=ω(loglogN). Furthermore, the vertices of these graphs can be represented by string of length 2log2N, and the incidence function of these graphs can be computed by Boolean circuits of size poly(logN).

Original languageEnglish
Title of host publicationComputational Complexity and Property Testing
Subtitle of host publicationOn the Interplay Between Randomness and Computation
EditorsOded Goldreich
PublisherSpringer Nature Switzerland AG
Pages363-373
Number of pages11
ISBN (Electronic)978-3-030-43662-9
ISBN (Print)978-3-030-43661-2
DOIs
StatePublished - 1 Jan 2020

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume12050 LNCS
ISSN (Print)0302-9743

All Science Journal Classification (ASJC) codes

  • Theoretical Computer Science
  • General Computer Science

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