Circuits on Cylinders

We consider the computational power of constant width polynomial size cylindrical circuits and nondeterministic branching programs. We show that every function computed by a \({\bf \prod}_2 \circ {\bf MOD} \circ {\bf AC}^0\) circuit can also be computed by a constant width polynomial size cylindrical nondeterministic branching program (or cylindrical circuit) and that every function computed by a constant width polynomial size cylindrical circuit belongs to ACC 0.