Inverting and Minimalizing Path Sets and Cut Sets

This paper describes a technique for generating the minimal cuts from the minimal paths, or vice versa, for s-coherent systems. The process is a recursive 2-stage expansion based upon de Morgan's theorems; ie, it is the inversion of a Boolean polynomial having all common-valued (either all 0 or all 1) components, so that the inverse also has only common-valued components of the opposite sign. There are procedural short cuts and Quine-type absorptions; absorptions put the polynomial into its minimalized form. The number of stages of recursion is equal to the number of terms (minimal states) in the starting polynomial. The minimal states of the inverse form are the terms of the inverse polynomial after minimalization. Since the system is s-coherent and all components are common-valued in either the original or Inverse minimal forms, the lists of minimal states are unique.