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. Complexity3 (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 knq-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.