  It is known that there are classes of 2-CNFs requiring exponential size
non-deterministic read-once branching programs to compute them. However, to the
best of our knowledge, there are no superpolynomial lower bounds for branching
programs of a higher repetition computing a class of 2-CNFs. This work is an
attempt to make a progress in this direction.
  We consider a class of monotone 3-CNFs that are almost 2-CNFs in the sense
that in each clause there is a literal occurring in this clause only. We prove
exponential lower bounds for two classes of non-deterministic branching
programs. The first class significantly generalizes monotone read-$k$-times
{\sc nbp}s and the second class generalizes oblivious read $k$ times branching
programs. The lower bounds remain exponential for $k \leq \log n/a$ where $a$
is a sufficiently large constant.
