Superlinear Lower Bounds for Bounded-Width Branching Programs

We use algebraic techniques to obtain superlinear lower bounds on the size of bounded-width branching programs to solve a number of problems. In particular, we show that any bounded-width branching program computing a nonconstant threshold function has length Ω(n log log n), improving on the previous lower bounds known to apply to all such threshold functions. We also show that any program over a finite solvable monoid computing a product in a nonsolvable group has length Ω(n log log n). This result is a step toward proving the conjecture that the circuit complexity class ACC0 is properly contained in NC1.