Effective conductances of Moore-Shannon hammocks

By assuming each device in a Moore-Shannon hammock network to have a finite conductance g when closed, we decompose the reliability polynomial h(p,q), associated with the hammock network, as a sum of terms representing the possible nonzero values of G /g (where G is the effective conductance between the terminals S and T of the hammock). We then compute the expected value of G/g. We also compute G in the more general case, in which the devices may have distinct conductances. Our calculations are exact, as opposed to numerical. Such decompositions are meant to help us gain insights into the still unexplained optimality of the Moore-Shannon hammocks. The results should also be useful for designers of nano-electromechanical systems (NEMS).