Subquadratic Simulations of Balanced Formulae by Branching Programs

This paper considers Boolean formulae and their simulations by bounded width branching programs. It is shown that every balanced Boolean formula of size $s$ can be simulated by a constant width (width 5) branching program of length $s^{1.811\ldots}$. A lower bound for the translational cost from formulae to permutation branching programs is also presented.