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 + ǫ)n, for some constant ǫ > 0. We also give the first separation result between the syntactic and semantic read-k models [BRS93] 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 [BRS93]: 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).