Dawar and Wilsenach (ICALP 2020) introduce the model of symmetric arithmetic circuits and show an exponential separation between the sizes of symmetric circuits for computing the determinant and the permanent. The symmetry restriction is that the …
We introduce symmetric arithmetic circuits, i.e. arithmetic circuits with a natural symmetry restriction. In the context of circuits computing polynomials defined on a matrix of variables, such as the determinant or the permanent, the restriction …