Totally positive view of a computer microchip

We define semiconductor networks, which serve as a model for computer microchips, and discuss the inverse boundary problem for these networks. Simply speaking, we answer the question: "To which extent and how can we identify a computer microchip by boundary measurements?" Interestingly, the theory of semiconductor networks generalizes (and simplifies) the recent results of Berenstein, Fomin, and Zelevinsky on totally positive matrices and double Bruhat cells. Let us say that a matroid on an ordered set is totally positive if it can be represented by a real k x n matrix with nonnegative maximal minors. The combinatorial classes of semiconductor networks are in one-to-one correspondence with totally positive matroids. A byproduct of our theory is the complete combinatorial description of totally positive matroids.