The authors use algebraic techniques to obtain superlinear lower bounds on the size of bounded-width branching programs to solve a number of problems. In particular, they show that any bounded-width branching program computing a nonconstant threshold function has length Omega (n log log n), improving on the previous lower bounds known to apply to all such threshold functions. They also show that any program over a finite solvable monoid computing products in a nonsolvable group has length Omega (n log log n). This result is a step toward proving the conjecture that the circuit complexity class ACC/sup 0/ is properly contained in NC/sup 1/.
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