Time-space Tradeoos for Branching Programs

We obtain the rst non-trivial time-space tradeoo lower bound for functions f : f0;1g n ! f0;1g on general branching programs by exhibiting a Boolean function f that requires exponential size to be computed by any branching program of length (1 +)n, for some constant > 0. We also give the rst 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 tradeoo 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).