Tree Petri Nets: Properties and Applications in Logical Problems

A special subclass of Petri net, tree Petri net, is discussed. For a tree Petri net, a marking M₁ is reachable from M₂ if and only if M₂ is reachable from M₁ in its inversed Petri net, and the reach ability is equivalent to the state equation satisfiability. Furthermore, two applications of tree Petri nets in logical problems´ analysis are presented. One is applied to the calculation of minimal cut sets of coherent fault tree, the other is used to solve an and-or tree. The corresponding algorithms are given. It is demonstrated that the tree Petri net is effective for failure analysis and artificial intelligence problem solution. Some examples are presented to validate these conclusions.