Guessing secrets efficiently via list decoding (extended abstract)

Noga Alon, Venkatesan Guruswami, Tali Kaufman, Madhu Sudan

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

19 Scopus citations

Abstract

We consider the guessing secrets problem defined by Chung, Graham, and Leighton [CGL01]. This is a variant of the standard 20 questions game where the player has a set of k > 1 secrets from a universe of N possible secrets. The player is asked Boolean questions about the secret for each question, the player picks one of the k secrets adversarially, and answers according to this secret. We present an explicit set of O(logiV) questions together with an efficient (i.e., poly (log AT) time) algorithm to solve the guessing secrets problem for the case of 2 secrets. This answers the main algorithmic question left unanswered by [CGL01]. The main techniques we use are small e-biased spaces and the notion of list decoding. We also establish bounds on the number of questions needed to solve the A;-secrets game for k > 2, and discuss how list decoding can be used to get partial information about the secrets.

Original languageEnglish (US)
Title of host publicationProceedings of the 13th Annual ACM-SIAM Symposium on Discrete Algorithms, SODA 2002
PublisherAssociation for Computing Machinery
Pages254-262
Number of pages9
ISBN (Electronic)089871513X
StatePublished - Jan 1 2002
Externally publishedYes
Event13th Annual ACM-SIAM Symposium on Discrete Algorithms, SODA 2002 - San Francisco, United States
Duration: Jan 6 2002Jan 8 2002

Publication series

NameProceedings of the Annual ACM-SIAM Symposium on Discrete Algorithms
Volume06-08-January-2002

Other

Other13th Annual ACM-SIAM Symposium on Discrete Algorithms, SODA 2002
CountryUnited States
CitySan Francisco
Period1/6/021/8/02

All Science Journal Classification (ASJC) codes

  • Software
  • Mathematics(all)

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