Two types of branching programs with bounded repetition that cannot efficiently compute monotone 3-CNFs

We prove exponential lower bounds for two classes of non-deterministic branching programs (nbps) with bounded repetition computing a class of functions representable by monotone 3-cnfs. The first class significantly generalizes monotone read-k-times nbps and the second class generalizes oblivious read k times branching programs. To the best of our knowledge, this is the first separation of monotone nbps with bounded repetition from monotone cnfs as well as the first separation of oblivious read-ktimes branching programs (even determinisitc ones) from cnfs. The lower bounds remain exponential for k ≤ logn/a where a is a sufficiently large