A Polynomial Time Construction of a Hitting Set for Read-Once Branching Programs of Width 3

The relationship between deterministic and probabilistic computations is one of the central issues in complexity theory. This problem can be tackled by constructing polynomial time hitting set generators which, however, belongs to the hardest problems in computer science even for severely restricted computational models. In our work, we consider read-once branching programs for which such a construction has been known only in the case of width 2. We characterize the hitting sets for read-once branching programs of width 3 by a necessary and (in a certain sense) sufficient so-called richness condition which is independent of a notion of branching programs. Then, we prove that any almost (C log n)-wise independent set satisfies this richness condition for a suitable constant C. By using such a set due to Alon et al. (1992), our result provides an explicit polynomial time construction of a hitting set for read-once branching programs of width 3.