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 + epsilon)n, for some constant epsilon > 0. We also give the first separation result between the syntactic and semantic read-k models [10] 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 [10]: 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).