Strong XOR Lemma for Communication with Bounded Rounds: (extended abstract)

Research output: Chapter in Book/Report/Conference proceedingConference contribution

2 Scopus citations

Abstract

In this paper, we prove a strong XOR lemma for bounded-round two-player randomized communication. For a function f:X×Y?{0,1}, the n-fold XOR function f?n: Xn× Yn ? {0,1} maps n input pairs (X1,. . . , Xn, Y1,. . ., Yn) to the XOR of the n output bits f(X1, Y1)?. . .? f(Xn, Yn). We prove that if every r-round communication protocols that computes f with probability 2/3 uses at least C bits of communication, then any r-round protocol that computes f? n with probability 1/2+exp(-O(n)) must use n (r-O(r) C-1) bits. When r is a constant and C is sufficiently large, this is O(n C) bits. It matches the communication cost and the success probability of the trivial protocol that computes the n bits f(Xi, Yi) independently and outputs their XOR, up to a constant factor in n. A similar XOR lemma has been proved for f whose communication lower bound can be obtained via bounding the discrepancy [17]. By the equivalence between the discrepancy and the correlation with 2-bit communication protocols [19], our new XOR lemma implies the previous result.

Original languageEnglish (US)
Title of host publicationProceedings - 2022 IEEE 63rd Annual Symposium on Foundations of Computer Science, FOCS 2022
PublisherIEEE Computer Society
Pages1186-1192
Number of pages7
ISBN (Electronic)9781665455190
DOIs
StatePublished - 2022
Event63rd IEEE Annual Symposium on Foundations of Computer Science, FOCS 2022 - Denver, United States
Duration: Oct 31 2022Nov 3 2022

Publication series

NameProceedings - Annual IEEE Symposium on Foundations of Computer Science, FOCS
Volume2022-October
ISSN (Print)0272-5428

Conference

Conference63rd IEEE Annual Symposium on Foundations of Computer Science, FOCS 2022
Country/TerritoryUnited States
CityDenver
Period10/31/2211/3/22

All Science Journal Classification (ASJC) codes

  • General Computer Science

Keywords

  • communication complexity
  • xor lemma

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