Cycle inclusion property of augmented marked graphs

A cycle-inclusion property which characterizes the siphon-trap property, liveness, and reversibility for augmented marked graphs, is described. It examines the pre-sets, post-sets, and their inclusion for a subset of cycles so checking of liveness and reversibility can be based on cycles. It is found that finding cycles is simpler than finding siphons and traps and that checking the cycle-inclusion property is simpler than checking the siphon-trap property or the potential emptiness of siphons. In system design, liveness and reversibility are essential attributes of the design correctness. This is especially important for systems with shared resources, such as manufacturing systems.