We obtain the first non-trivial time-space tradeoff lower bound for
functions f:{0,1}^n ->{0,1} on general branching programs by exhibiting a
Boolean function f that requires exponential size to be computed by any
branching program of length cn, for some constant c>1. We also give the first
separation result between the syntactic and semantic read-k models for k>1 by
showing that polynomial-size semantic read-twice branching programs can compute
functions that require exponential size on any syntactic read-k branching
program. We also show a time-space tradeoff result on the more general
R-way branching program model: for any k, we give a function that requires
exponential size to be computed by length kn q-way branching programs, for
some q=q(k).
