Time-space tradeoffs for branching programs

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+ε)n, for some constant ε>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. 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)