Petri sub-nets for minpath-based fault trees

The choice of proper forms of fault tree (FT) and success tree (ST) representations, respectively inside of Petri nets (PNs) in the field of R&M modeling is not a trivial problem, because there is the danger of stray tokens inside of the sub-PNs of those trees which would disturb the system model's proper operation in the long run. The author has been advocating the use of disjunctive normal forms (DNFs=sum-of-products forms). However, typically in the field of graph connectivity problems the initially found FTs usually result from minpaths rather than from mincuts. The Boolean FT functions are therefore initially conjunctive normal forms (CNFs=product-of-sums forms). As the main result of this paper it is shown that for such FTs, sub-PNs can be designed systematically, even though they are not quite as simple as sub-PNs for FTs of DNFs. The main point is to allow for extra FT input places, and to gather all the tokens corresponding to the single variables of the diverse sums once the repairs of the corresponding components are finished. This way no stray tokens remain inside of the FT's sub-PN. As a consequence of the duality between FTs and STs, and since both "trees" are usually inserted in the overall system PN model, it suffices to find a DNF or a CNF of either tree's Boolean function. A CNF or a DNF of the other tree is then readily found via Shonnon's inversion theorem, i.e., it needs no complex Boolean algebra manipulations. The general results are formulated as PN design rules.