  In this paper we establish an exponential lower bound on the size of
syntactic non-deterministic read $d$-times branching programs for $d \leq \log
n /10^5$ computing a class of monotone CNFs with a linear number of clauses.
This result provides the first separation of classes NP and co-NP for syntactic
branching programs with a logarithmic repetition and the first separation of
syntactic non-deterministic branching programs with a logarithmic repetition
from small monotone CNFs.
