New Lower Bounds and Hierarchy Results for Restricted Branching Programs

摘要

In unrestricted branching programs all variables may be tested arbitrarily often on each path. But exponential lower bounds are only known if on each path the number of tests of each variable is bounded. We examine branching programs in which for each path the number of variables that are tested more than once is bounded bykbut we do not bound the number of tests of those variables. Using a new lower bound method we can prove that such branching programs become more powerful by increasingkonly by 1: Fork⩽(1−ε)(n/3)(1/3)/log2/3 n, whereε>0, we exhibit Boolean functions that can be represented in polynomial size ifkvariables may be tested more than once on each path, but only in exponential size ifk−1 variables may be tested more than once on each path. Therefore, we obtain a tight hierarchy.