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In their seminal paper, Valiant, Skyum, Berkowitz and Rackoff proved that arithmetic circuits can be balanced [VSBR]. That is, [VSBR] showed that for every arithmetic circuit of ...
We construct an explicit polynomial f(x1, . . . , xn), with coefficients in {0, 1}, such that the size of any syntactically multilinear arithmetic circuit computing f is at least ...
Abstract. We study structural properties of restricted width arithmetical circuits. It is shown that syntactically multilinear arithmetical circuits of constant width can be effici...
Algorithmic tools for graphs of small treewidth are used to address questions in complexity theory. For both arithmetic and Boolean circuits, it is shown that any circuit of size ...
We initiate a direction for proving lower bounds on the size of non-commutative arithmetic circuits. This direction is based on a connection between lower bounds on the size of no...