Time-space tradeoffs for branching programs

Abstract

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 (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 tradeoff for decision problems in this model.