We show that, over an arbitrary ring, for any fixed ∈>0, all balanced algebraic formulas of sizes are computed by algebraic straight-line programs that employ a constant number of registers and have lengthO (s 1+∈). In particular, in the special case where the ring isGF(2), we obtain a technique for simulating balanced Boolean formulas of sizes by bounded-width branching programs of lengthO(s 1+∈), for any fixed ∈>0. This is an asymptotic improvement in efficiency over previous simulations in both the Boolean and algebraic settings.
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