  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 non-binary sequences. We show that unlike
the binary case, deterministic randomness extraction in the generalized case is
sometimes possible. We present a necessary condition and a sufficient condition
for the possibility of deterministic randomness extraction. These two
conditions coincide in "non-degenerate" cases.
  Next, we turn to a distributed setting. In this setting the SV source
consists of a random sequence of pairs $(a_1, b_1), (a_2, b_2), \ldots$
distributed between two parties, where the first party receives $a_i$'s and the
second one receives $b_i$'s. The goal of the two parties is to extract common
randomness without communication. Using the notion of maximal correlation, we
prove a necessary condition and a sufficient condition for the possibility of
common randomness extraction from these sources. Based on these two conditions,
the problem of common randomness extraction essentially reduces to the problem
of randomness extraction from (non-distributed) SV sources. This result
generalizes results of G\'acs and K\"orner, and Witsenhausen about common
randomness extraction from i.i.d. sources to adversarial sources.
