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 prove optimal lower bounds for multilinear circuits and for monotone circuits with bounded depth. These lower bounds state that, in order to compute certain functions, these cir...
We show that proving exponential lower bounds on depth four arithmetic circuits imply exponential lower bounds for unrestricted depth arithmetic circuits. In other words, for expo...
We study families of Boolean circuits with the property that the number of gates at distance t fanning into or out of any given gate in a circuit is bounded above by a polynomial ...