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 ...
We prove an exponential lower bound for the size of constant depth multilinear arithmetic circuits computing either the determinant or the permanent (a circuit is called multiline...
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 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...
Motivated by the Hadamard product of matrices we define the Hadamard product of multivariate polynomials and study its arithmetic circuit and branching program complexity. We also...
Vikraman Arvind, Pushkar S. Joglekar, Srikanth Sri...