Lower Bounds for Syntactically Multilinear Algebraic Branching Programs
نویسنده
چکیده
It is shown that any weakly-skew circuit can be converted into a skew circuit with constant factor overhead, while preserving either syntactic or semantic multilinearity. This leads to considering syntactically multilinear algebraic branching programs (ABPs), which are defined by a natural read-once property. A 2 size lower bound is proven for ordered syntactically multilinear ABPs computing an explicitly constructed multilinear polynomial in 2n variables. Without the ordering restriction a lower bound of level Ω(n/ log n) is observed, by considering a generalization of a hypercube covering problem by Galvin [1].
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