Identification of Symmetry, Redundancy and Equivalence of Boolean Functions

Abstract

Functionally packaged logic can only be effectively utilized if the totality of switching functions that each package is capable of providing is recognized. Theorems concerning, and algorithms operating on, multiple output switching functions (possibly with don't care conditions) in cubical array notation are presented that 1) detect partial symmetry and redundancy sets of input varibles, 2) determine the function generated by a package with some of its inputs tied to logical 1 or 0 or tied together, and 3) rapidly show equivalence between two functions using symmetry information. While manual execution of the algorithms is possible, they are computer oriented. Results from actual computer experimentation show their efficiency.