Deterministic Randomness Extraction from Generalized and Distributed Santha--Vazirani Sources
Salman Beigi, Omid Etesami, Amin Gohari · SIAM Journal on Computing · 2017
A Santha--Vazirani (SV) source is a sequence of random bits where the conditional distribution of each bit, given the previous bits, can be partially controlled by an adversary. Santha and Vazirani show that deterministic randomness extraction from these sources is impossible. In this paper, we study the generalization of SV sources for nonbinary sequences. We show that unlike the binary setup of Santha and Vazirani, deterministic randomness extraction in the generalized case is sometimes possible. In particular, if the adversary has access to $s$ “nondegenerate” dice that are $c$-sided and can choose one die to throw based on the previous realizations of the dice, then deterministic randomness extraction is possible if $s