The Minimization of Inverters in Analog Computer Programming

An algorithm is described for determining the least number of inverters required in an analog (or analog/hybrid) computer circuit for a general problem. The procedure requires the creation of a dependency matrix for the problem which reflects the interdependencies among the problem variables. Various modifications to this matrix are then made to produce a modified dependency matrix (MDM). The problem of minimizing the circuit inverters is then shown to be equivalent to minimizing a particular attribute of MDM referred to as its cost index. A necessary condition which must be satisfied at the minimum cost index is formulated and this necessary condition is used to guide the algorithm. A flowchart for the procedure is given and the computational results for a representative example problem are also included.