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 (A. Borodin et al., Comput. Complexity 3 (1993), 1-18) for k > 1 by showing that polynomial-size semantic read-twice branching programs can compute functions that require exponential size on any semantic read-k branching program. We also show a time-space tradeoff result on the more general R-way branching program model (Borodin et al., 1993): 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). This result gives a similar tradeoff for RAMs, and thus provides the first nontrivial time-space tradedoff for decision problems in this model. (C) 2001 Elsevier Science (USA).