Petri net is a graphical and mathematical tool for modelling, analysis, verification, and evaluation of discrete event systems. Liveness is one of the most important problems of Petri net analysis. This is concerned with a capability for firing of transitions and can be interpreted as a problem to decide whether the system under consideration is always able to reach a stationary behavior, or to decide whether the system is free from any redundant elements. An asymmetric choice (AC) net is a superclass of useful subclasses such as EFCs, FCs, SMs, and MGs, where SMs admit no synchronization, MGs admit no conflicts, FCs as well as EFCs admit no confusion, and ACs allow asymmetric confusion but disallow symmetric confusion. It is known that an AC net N is live iff it is place-live, but this is not the "initial-marking-based" condition and place-liveness is in general hard to test. For the initial-marking-based liveness for AC nets, it is only known that an AC net N is live if (but not only if) every deadlock in N contains a marked structural trap.