INVERTING AND MINIMIZING BOOLEAN FUNCTIONS, MINIMAL PATHS AND MINIMAL CUTS - NONCOHERENT SYSTEM-ANALYSIS

An efficient technique is presented for inverting the minimal paths of a reliability logic diagram or fault tree, and then minimizing to obtain the minimal cuts, or else inverting the minimal cuts for the minimal paths. The method is appropriate for both s-coherent and s-noncoherent systems; it can also obtain the minimized dual inverse of any Boolean function. Inversion is more complex with s-noncoherence than with s-coherence because the minimal form (m.f.) is not unique. The result of inversion is the dual prime implicants (pi.‘s). The terms of a dual m.f., the dual minimal states, are obtained By a search process. First the dual p.i.'s are obtained; then a m.f. is found by an algorithmic search with a test for redundancy, reversal-absorption (ra.). The dual p.i.'s are segregated into the “core” p.i.'s [8, 9] essential for every m.f. and the “noncore” p.i.'s, by ra. Then a m.f. is found by repeatedly applying ra. to randomized rearrangements of the noncore terms. Examples are included, adapted from the fault-tree literature. Copyright © 1979 by the Institute of Electrical and Electronics Engineers, Inc.