Public vs private coin in bounded-round information

Mark Braverman, Ankit Garg

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

17 Scopus citations

Abstract

We precisely characterize the role of private randomness in the ability of Alice to send a message to Bob while minimizing the amount of information revealed to him. We give an example of a (randomized) message which can be transmitted while revealing only I bits of information using private randomness, but requires Alice to reveal I + logI - O(1) bits of information if only public coins are allowed. This gives the first example of an ω(1) additive separation between these two models. Our example also shows that the one-round compression construction of Harsha et al. [HJMR07] cannot be improved. Moreover, we show that our example is tight up to an additive O(1) factor: We show that if using private randomness a message can be transmitted while revealing I bits of information, the transmission can be simulated without private coins using I + logI + O(1) bits of information. This improves over an earlier result by Brody et al. [BBK+12].

Original languageEnglish (US)
Title of host publicationAutomata, Languages, and Programming - 41st International Colloquium, ICALP 2014, Proceedings
PublisherSpringer Verlag
Pages502-513
Number of pages12
EditionPART 1
ISBN (Print)9783662439470
DOIs
StatePublished - Jan 1 2014
Event41st International Colloquium on Automata, Languages, and Programming, ICALP 2014 - Copenhagen, Denmark
Duration: Jul 8 2014Jul 11 2014

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
NumberPART 1
Volume8572 LNCS
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349

Other

Other41st International Colloquium on Automata, Languages, and Programming, ICALP 2014
CountryDenmark
CityCopenhagen
Period7/8/147/11/14

All Science Journal Classification (ASJC) codes

  • Theoretical Computer Science
  • Computer Science(all)

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