TY - JOUR

T1 - Guessing secrets efficiently via list decoding

AU - Alon, Noga

AU - Guruswami, Venkatesan

AU - Kaufman, Tali

AU - Sudan, Madhu

PY - 2007/11/1

Y1 - 2007/11/1

N2 - We consider the guessing secrets problem defined by Chung et al. [2001]. 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(log N) questions together with an efficient (i.e., poly(log N) time) algorithm to solve the guessing secrets problem for the case of 2 secrets. This answers the main algorithmic question left unanswered by Chung et al. [2001]. The main techniques we use are small ε-biased spaces and the notion of list decoding.

AB - We consider the guessing secrets problem defined by Chung et al. [2001]. 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(log N) questions together with an efficient (i.e., poly(log N) time) algorithm to solve the guessing secrets problem for the case of 2 secrets. This answers the main algorithmic question left unanswered by Chung et al. [2001]. The main techniques we use are small ε-biased spaces and the notion of list decoding.

KW - 20 questions

KW - Biased spaces

KW - Decoding algorithms

KW - Error-correcting codes

KW - K-universal sets

UR - http://www.scopus.com/inward/record.url?scp=36448962041&partnerID=8YFLogxK

U2 - 10.1145/1290672.1290679

DO - 10.1145/1290672.1290679

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AN - SCOPUS:36448962041

SN - 1549-6325

VL - 3

JO - ACM Transactions on Algorithms

JF - ACM Transactions on Algorithms

IS - 4

M1 - 1290679

ER -