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We study limitations of polynomials computed by depth-2 circuits built over read-once formulas (ROFs). In particular:

• We prove a 2^Ω(n) lower bound for the sum of ROFs computing the 2n-variate polynomial in VP defined by Raz and Yehudayoff [21].

• We ...

This work deals with the power of linear algebra in the context of multilinear computation. By linear algebra we mean algebraic branching programs (ABPs) which are known to be computationally equivalent to two basic tools in linear algebra: iterated ...

An arithmetic formula is multilinear if the polynomial computed by each of its subformulas is multilinear. We prove that any multilinear arithmetic formula for the permanent or the determinant of an n × n matrix is of size super-polynomial in n. ...

An arithmetic formula is multi-linear if the polynomial computed by each of its sub-formulas is multi-linear. We prove that any multi-linear arithmetic formula for the permanent or the determinant of an n x n matrix is of size super-polynomial in ...