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 3 p -circuits, the function f has nondeterministic BP1s (with one nondeterministic node) of linear size and f has size O ( n 4 ) for oblivious nondeterministic BP1s but f requires nondeterministic graph-driven BP1s of size 2 ( n ) . This answers an open question stated by Jukna, Razborov, Savick'y, and Wegener (1999).