The Lattice-Grid Network and its Applications to the Minimization and Threshold-Gate Realization of Boolean Switching Functions.

The Lattice-Grid Network LGN is a 2-dimensional representation of the n-cube that is theoretically unbounded in the finite number of dimensions variables for which it can be constructed. The basis of the construction technique is that each row of the LGN contains all the vertices minterms that have the same number of 1 coordinates uncomplemented variables. Techniques similar to those used with a Karnaugh Map are used with the LGN for the minimization of completely and incompletely specified Boolean functions of either single or multiple outputs. The LGN is also used to identify and determine the realization of threshold functions. A characteristic measure of the function is determined, using a small fraction of the vertices of the function, to identify 2-monotonicity and evaluate the weights in the realization of the function. n2-monotonicity, the final step in the process of identifying a threshold function, is determined using a visual technique of comparing the function with its dual. Author