Abstract
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 (1+c)n, for some constant c>0. 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. In addition we show a time-space tradeoff result on the more general R-way branching program model: for any k, we exhibit a function that requires exponential size to be computed by length kn q-way branching programs, for some q=q(k).