Almost k-Wise Independent Sets Establish Hitting Sets for Width-3 1-Branching Programs

Recently, an interest in constructing pseudorandom or hitting set generators for restricted branching programs has increased, which is motivated by the fundamental problem of derandomizing space bounded computations. Such constructions have been known only in the case of width 2 and in very restricted cases of bounded width. In our previous work, we have introduced a so-called richness condition which is, in a certain sense, sufficient for a set to be a hitting set for read-once branching programs of width 3. In this paper, we prove that, for a suitable constant C, any almost C log n-wise independent set satisfies this richness condition. Hence, we achieve an explicit polynomial time construction of a hitting set for read-once branching programs of width 3 with the acceptance probability greater than p 12/13 by using the result due to Alon et al. (1992).