I'm working on a problem where the formalism appears to be an abstraction of a kind of Petri net, and it is possible to construct an equivalent Petri net from this formalism with the same behavior. The Petri net that is constructed is bounded, and a transition is either $L0$-Live or $L1$-Live. So in this net, a transition fires only once or not at all.
I've looked into the coverability of Petri nets and it appears that the coverability problem in general has $\text{EXPSPACE}$ complexity (https://www7.in.tum.de/~blondin/papers/BFHH16.pdf). However, I could not find any literature that relates the liveness of a Petri net to its coverability, and the impact on complexity. Is there any work that has looked into this?