A very simple function that requires exponential size nondeterministic graph-driven read-once branching programs

摘要

Branching programs are a well-established computation model for Boolean functions, especially read-once branching programs (BP1s) have been studied intensively. A very simple function f in n~2 variables is exhibited such that both the function f and its negation -f can be computed by Σ_p~3-circuits, the function f has nondeterministic BP1s (with one nondeterministic node) of linear size and -f has size O(n~4) for oblivious nondeterministic BPls but f requires nondeterministic graph-driven BP1s of size 2~(Ω(n)). This answers an open question stated by Jukna, Razborov, Savicky, and Wegener [Comput. Complexity 8 (1999)357-370].