A Polynomial Time Constructible Hitting Set for Restricted 1-Branching Programs of Width 3

Abstract

An important problem in complexity theory is to find polynomial time constructible hitting sets for Boolean functions in different standard models. This would have consequences for the relationship between deterministic and probabilistic computations in the respective models. Using the result by Alon, Goldreich, Håstad, and Peralta (1992) we provide a polynomial time constructible hitting set for restricted read-once branching programs of width 3. The restriction excludes only one from all patterns of level-to-level transitions in a normalized form of 3-width 1-branching programs. In fact, our technique works for a slightly more general class of such programs. Although this restriction seems to be relatively strong our proof reveals the core of difficulties and thus represents the first step for proving the result for less restricted models.