Resistive circuit topologies that admit several solutions

Necessary and sufficient conditions are given that a resistive circuit may have several but finitely many solutions. Whether it actually has several solutions depends on the values of the sources and linear resistors as well as on the characteristics of the non-linear resistors. Such circuits are required for static memory applications of all kinds, including associative memories realized by neural networks. These criteria are given both in terms of linear circuits and circuit topology. In the same way the minimal memory circuits are characterized. They constitute the building blocks for more complicated memory circuits.